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axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
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Some of my NBA capper friends have been asking about MLB. I wrote this for 2007 using 2006 data but I believe the same principles still apply. The graphs do not show up correctly and tables aren't formatted but I have a .doc copy for those that want it. Best of luck this season and again, this is only for beginners and not the more seasoned capper.

:)
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<o:p></o:p>
<o:p>Ok, I have to post this in sections.</o:p>
<o:p></o:p>
<o:p>Also had to do in IE. I'm a chrome user and nogo for that browser.</o:p>
 
Last edited:
MadJack

MadJack

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go into your "edit options" in User CP and make this change. "Enhanced Interface" then things should format for you properly when posting to a thread.

<TABLE class=tborder cellSpacing=1 cellPadding=6 width="100%" align=center border=0><TBODY><TR><TD class=thead>Miscellaneous Options </TD></TR><TR><TD class=panelsurround align=middle>
<FIELDSET class=fieldset><LEGEND><LABEL for=sel_showvbcode>Message Editor Interface</LABEL></LEGEND><TABLE cellSpacing=3 cellPadding=0 width="100%" border=0><TBODY><TR><TD>When posting messages to the forums or other members, there are three interface types available to you. The simplest of these is a simple text box, while the last is a fully-fledged WYSIWYG editor, which allows you to format your text as you want it and see the results immediately.

Depending upon the capabilities of your web browser, you may not be able to use all of these options. If you experience problems when posting messages, try switching to a different interface type.</TD></TR><TR><TD><SELECT id=sel_showvbcode name=showvbcode> <OPTION value=0>Basic Editor - A simple text box</OPTION> <OPTION value=1>Standard Editor - Extra formatting controls</OPTION> <OPTION value=2 selected>Enhanced Interface - Full WYSIWYG Editing</OPTION></SELECT> <LABEL for=sel_showvbcode>Message Editor Interface:</LABEL> </TD></TR></TBODY></TABLE></FIELDSET>​

<INPUT class=button accessKey=s type=submit value="Save Changes"> <INPUT class=button accessKey=r type=reset value="Reset Fields">
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axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
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0
Taxachusetts
MAJOR LEAGUE BASEBALL WINS
AND THE ROAD TO THE PLAYOFFS


<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>
OVERVIEW... 3<o:p></o:p>
DESCRIPTIVE ANALYSIS-MLB WINS. 4<o:p></o:p>
FREQUENCY DISTRIBUTION ? MLB.. 5<o:p></o:p>
HYPOTHESIS TESTS - MLB.. 6<o:p></o:p>
MULTIPLE REGRESSION MODEL ? MLB.. 8<o:p></o:p>
Adjusted Projected Wins. 10<o:p></o:p>
SUMMARY.. 11<o:p></o:p>
DATA.. 11<o:p></o:p>

<o:p></o:p>​




<o:p></o:p>​

OVERVIEW

The following analysis uses Major League Baseball (MLB) data compiled for the 2006 season and retrieved from Yahoo! Sports. The sample consists of all 30 major league teams for 2006. Observations of each team include categorical variables such total wins (W), team batting average (AVG), home runs (HR), stolen bases (SB), earned run average (ERA), walk/hits per innings pitched (WHIP) and league.
W represents the number of times a team scores more runs than its opponent by the end of each game-play during the course of a 162 game season.
AVG represents team batting proficiency by calculating the number of hits per at-bats. A hit means that the batter reaches base while putting the ball in play and not due to an error or a fielder?s choice. An at-bat should not be confused with a plate appearance. All at-bats are plate appearances but the reverse does not hold true. For more detailed explanations, the reader should consult the official rules of MLB.
HR measures power. An HR is at least one run on the scoreboard as a result of a hit by a batter and the run scored by the same batter.
SB are credited for base advancement while the ball is not in play and not due to other factors such as a wild pitch, pass ball or defensive indifference. This is a measure of speed. Further information on SB is available by consulting any number of MLB related references.
ERA and WHIP are pitching statistics. ERA calculates earned runs given up to opposing teams. WHIP measures the number of batters allowed to reach base via hits and walks. ERA is per 9 innings and WHIP is per inning. The importance of these categories is their indicative measure of yielded earned runs and possible runs to an opposing team. Again, detailed information is available from a variety of sources.
League categorizes each team as either American (AL) or National (NL). Rules are generally similar in each league. I felt it was important to designate league membership since the <?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:eek:ffice:smarttags" /><st1:State w:st="on"><st1:place w:st="on">AL</st1:place></st1:State> comprises of 14 teams while the NL has 16. This comes into play because only 4 teams from each league will earn the opportunity to participate in the playoffs to determine which team from each league will play in the World Series, the MLB championship.


DESCRIPTIVE ANALYSIS-MLB WINS

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Measures of Central Tendency ? MLB<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 142.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=189>Mean<o:p></o:p>
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80.97<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 142.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=189>Median<o:p></o:p>
​
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80.00<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 142.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=189>Mode<o:p></o:p>
​
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76.00<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 4; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 142.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=189>Midrange<o:p></o:p>
​
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79.00<o:p></o:p>​


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<o:p></o:p>
The measures of central tendency take into account all the observations from the sample and give us a central reference point, an estimate of the normal value given the a set of numbers. The mean from the table above tells me that, on the average, a team will win about 81 games. This is interesting since a season is made up of 162 games. Yes, I understand that half of the games are won and half are lost. The interesting part is that with inter-league play, the means for each league can be different.
The mean statistic shows that an average team will win about half of their games. The mean is reliable since it takes into account every data element. It can have its drawbacks when extremes are involved.
The median shows that half of MLB teams will win more than 80 games and half will fail to reach the 80 win mark. This appears to fall in line with the mean calculations.
Mode reveals that 76 wins is the most common total among the 30 teams sampled. More teams accumulated 76 wins than any other total number of wins.
A midrange of 79 illustrates that, given the range of all team wins, 79 is the middle number. Range is defined shortly. The midrange is also prone to distortions if extreme data elements exist.
Given the statistics above, I can assume an average MLB team will win roughly 81 wins.
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Measures of Dispersion ? MLB<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 164.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=220>Range<o:p></o:p>
​
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36.00<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 164.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=220><st1:place w:st="on"><st1:placeName w:st="on">Interquartile</st1:placeName> <st1:placeType w:st="on">Range</st1:placeType></st1:place><o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 56.05pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=75>
12.00<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 164.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=220>Standard Deviation<o:p></o:p>
​
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10.08<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 164.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=220>Variance<o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 56.05pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=75>
101.69<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 164.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=220>Coefficient of Variation<o:p></o:p>
​
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12.45%<o:p></o:p>​


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<o:p></o:p>
Measures of dispersion describe the spread of the data or variation around the central value mentioned previously.
The range defines the difference between the lowest and highest values. It?s a simple measure of variation but only reports on extremes and does not provide information on the distribution of the remaining data. As shown under the table labeled ?Other Measures ? MLB?, the minimum wins for the 2006 season was 61 and the maximum was 97. The range therefore calculates to 36. Win totals for any team during this season falls in this range.
The interquartile range is another simple measure of variation. It eliminates extreme values by measuring only the range between the 25<SUP>th</SUP> percentile and the 75<SUP>th</SUP> percentile. By removing extreme values, the interquartile range yields the spread around the center region. As the table shows, this is a much narrower spread of 12 ranging from 76 to 88.
The variance and standard deviation are related measures of spread. Both measures take into consideration how the values distribute between extremes. This is done by measuring the ?average? scatter around the mean. Since the mean is the average, any summing calculations using distance from a value to the mean equals zero. Variance sums the squared differences between value and mean and then divides by one less than the total number of values. Rooting the variance then leads to the standard deviation.
In this study, values within one standard deviation will fall within plus/minus 10.08 around the mean. Two thirds of the observations fall within one standard deviation. This means that 20 teams? win total cluster around the 81 win mark give or take 10 games. Further, the statistics show that all teams will fall within 2 standard deviations from the center.
Another measure of variation is the coefficient of variation. This is a bit different in that it?s a relative measure expressed as a percentage of the mean. This sample indicates that data within 12.45% of the mean is said to be within one standard deviation. This is more useful when comparing data sets with different unit measures.
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 294.6pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=393 border=0><TBODY><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 149.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=199>Mean +/- 1 standard dev.<o:p></o:p>
​
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70.88<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=97>
91.05<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 222.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=296 colSpan=2># Observations within 1 standard dev.<o:p></o:p>
​
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20<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 149.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=199>Mean +/- 2 standard dev.<o:p></o:p>
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60.80<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=97>
101.13<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 222.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=296 colSpan=2># Observations within 2 standard dev.<o:p></o:p>
​
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30<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 149.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=199>Mean +/- 3 standard dev.<o:p></o:p>
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50.71<o:p></o:p>

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111.22<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 222.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=296 colSpan=2># Observations within 3 standard dev.<o:p></o:p>
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30<o:p></o:p>​


</TD></TR></TBODY></TABLE>
<o:p></o:p>
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 300.8pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=401 border=0><TBODY><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes; mso-row-margin-right: 6.2pt"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 222.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=296 colSpan=2>Other Measures - MLB<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=97 colSpan=2>
<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 0in; BORDER-TOP: #ece9d8; PADDING-LEFT: 0in; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent; mso-cell-special: placeholder" width=8>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 107.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=143>Sample Size<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 120.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=161 colSpan=2>
30<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=97 colSpan=2><o:p></o:p>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 107.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=143>Minimum<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 120.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=161 colSpan=2>
61.00<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=97 colSpan=2><o:p></o:p>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 107.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=143>Maximum<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 120.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=161 colSpan=2>
97.00<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=97 colSpan=2><o:p></o:p>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 107.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=143>First Quartile<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 120.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=161 colSpan=2>
76.00<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=97 colSpan=2><o:p></o:p>

</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 107.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=143>Third Quartile<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 120.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=161 colSpan=2>
88.00<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=97 colSpan=2><o:p></o:p>

</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 107.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=143>Given percentile =<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 120.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=161 colSpan=2>
73%<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=97 colSpan=2><o:p></o:p>

</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 7; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 107.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=143><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 120.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=161 colSpan=2>Value of percentile =<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 72.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=97 colSpan=2>
88<o:p></o:p>​


</TD></TR><TR height=0><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent" width=143></TD><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent" width=153></TD><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent" width=8></TD><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent" width=88></TD><TD style="BORDER-RIGHT: #ece9d8; BORDER-TOP: #ece9d8; BORDER-LEFT: #ece9d8; BORDER-BOTTOM: #ece9d8; BACKGROUND-COLOR: transparent" width=8></TD></TR></TBODY></TABLE>
<o:p></o:p>
The 73% given percentile is a value I chose because I wanted a quick number that gives me an idea of how many total wins an MLB club can set their sights on to have a legitimate chance of making the playoff. As previously mention, the AL and NL have different total number of teams but still, only 4 from each can qualify for the playoffs. Rather than analyzing each league individually, I chose to look at all teams as a whole. Therefore, only 8 teams from 30 will see post-season play. This number is 27% which means that 73% of teams will fall under a certain value. The value which 73% of teams will fall below is 88 games. A quick conclusion here is that to make the playoffs, a good number to work towards is at least 88 wins.
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
FREQUENCY DISTRIBUTION ? MLB

<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 5.4pt; WIDTH: 390.4pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=521 border=0><TBODY><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=58>
Lower<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>

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<o:p></o:p>

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Upper<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=92>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; mso-border-left-alt: solid windowtext .5pt" vAlign=bottom noWrap width=85>
Relative<o:p></o:p>

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Cumulative<o:p></o:p>

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Cum. Rel.<o:p></o:p>

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Limit<o:p></o:p>

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<o:p></o:p>

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Limit<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
Frequency<o:p></o:p>

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Frequency<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=89>
Frequency<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=85>
Frequency<o:p></o:p>

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40<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
48<o:p></o:p>

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0<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
0.0%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
0<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
0.0%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
48<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
56<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
0<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
0.0%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
0<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
0.0%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
56<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
64<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
2<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
6.7%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
2<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
6.7%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
64<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
72<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
4<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
13.3%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
6<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
20.0%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
72<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
80<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
8<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
26.7%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
14<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
46.7%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 7"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
80<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
88<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
7<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
23.3%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
21<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
70.0%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 8"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
88<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
96<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
6<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
20.0%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
27<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
90.0%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 9"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
96<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
104<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
3<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
10.0%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
30<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
100.0%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 10"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
104<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
112<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
0<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
0.0%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
30<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
100.0%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 16.5pt; mso-yfti-irow: 11"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
112<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=54>
< X <<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 16.5pt" vAlign=bottom noWrap width=58>
120<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=92>
0<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
0.0%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=89>
30<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 16.5pt" vAlign=bottom noWrap width=85>
100.0%<o:p></o:p>​

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</TD></TR><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 12"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=58>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=54>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=58>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=92>
30<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt" vAlign=bottom noWrap width=85>
100%<o:p></o:p>​

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=89>
<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=85><o:p></o:p>
​
</TD></TR><TR style="HEIGHT: 15pt; mso-yfti-irow: 13; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=58>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=54>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 43.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=58>
<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #69ffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 69.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15pt" vAlign=bottom noWrap width=92>sample size<o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=85><o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 66.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=89>
<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 63.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=85><o:p></o:p>

</TD></TR></TBODY></TABLE>​
<o:p></o:p>
The table above is a summary in which the data are arranged into numerically ordered class groupings. When determining the width of class interval, I made a couple of considerations. First, I wanted to make sure that 88 was a specified boundary. This figure was considered due to its significance in a team?s ideal target to get into the playoffs. I also accounted for the two extremes from MLB?s history in 162 game seasons. MLB didn?t always have 162 games and for convenience sake, I took the record low and record high in wins. The extreme figures are 43 and 116 record low and high respectively. The table shows that 9 teams had at least 88 wins. This error may be due to the difference in league make up. Using only analysis performed thus far, if a team manages at least 88 wins, it has an 8/9 chance of making the playoffs.
<o:p></o:p>
<?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /><v:shapetype id=_x0000_t75 stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"><v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f"></v:path><o:lock aspectratio="t" v:ext="edit"></o:lock></v:shapetype><v:shape id=_x0000_i1025 style="WIDTH: 417.75pt; HEIGHT: 222pt" type="#_x0000_t75"><v:imagedata o:title="" src="file:///C:\DOCUME~1\ADMINI~2.MCC\LOCALS~1\Temp\msohtml1\01\clip_image001.emz"></v:imagedata></v:shape><o:p></o:p>
<o:p></o:p>
This histogram is a graphical display of the frequency distribution table.
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
HYPOTHESIS TESTS - MLB

<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 5.4pt; WIDTH: 547.25pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=730 border=0><TBODY><TR style="HEIGHT: 20.25pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 375.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 20.25pt" vAlign=bottom noWrap width=501 colSpan=4>One Sample Hypothesis Test for the Mean<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 20.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 11.85pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.85pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=193><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.85pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.85pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.85pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 11.85pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>Null Hypothesis m =<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ffff99; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
88<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>Level of Significance<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ffff99; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
0.05<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>Sample Size<o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ffff99; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
30<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>Sample Mean<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ffff99; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
80.97<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>Standard Deviation<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ffff99; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
10.08<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 7"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=193><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 8"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>Test Statistic (Computed)<o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
-3.82<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 9"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=193><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 10"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=193><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>
​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 11"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>
Direction of Test<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
Lower Crit Value<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
Upper Crit Value<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=68>
p-Value<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>
Decision<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 12"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=193><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229>
<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 13"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>
Two-Tailed Test<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
-1.9600<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
1.9600<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=68>
0.0001<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>
Reject the null hypothesis<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 14"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>
H1: m <> 88<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229>
<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 15"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=193>
<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229>
<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 16"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>
Upper-Tail Test<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
n/a<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
1.6449<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=68>
0.9999<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>
Do not reject the null hypothesis<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 17"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=193>
H1: m > 88<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
​
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<o:p></o:p>

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<o:p></o:p>

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<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
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<o:p></o:p>

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<o:p></o:p>

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Lower-Tail Test<o:p></o:p>

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-1.6449<o:p></o:p>

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n/a<o:p></o:p>

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0.0001<o:p></o:p>

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Reject the null hypothesis<o:p></o:p>

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H1: m < 88<o:p></o:p>​


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 21"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 144.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=193><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

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If you REJECT the null hypothesis, conclude that H1 is true.<o:p></o:p>

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If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true.<o:p></o:p>

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NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).<o:p></o:p>​


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<o:p></o:p>
<o:p></o:p>
My first inquiry is how likely it is that the population win average is that magic number 88. The ?One Sample Hypothesis Test for the Mean? table above uses a level of significance of α = .05. α represents the probability of making a Type I error by rejecting the null hypothesis when it is true and should not be rejected. H<SUB>0</SUB>: m = 88 is rejected using the two tailed test. I conclude that in the history of MLB, the league has never averaged 88 wins. Out of curiosity, I asked if the number is above or below the magic number. The lower-tail test tells me to conclude that the number is smaller than 88.<o:p></o:p>
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 5.4pt; WIDTH: 552.05pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=736 border=0><TBODY><TR style="HEIGHT: 20.25pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 380.65pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 20.25pt" vAlign=bottom noWrap width=508 colSpan=4>One Sample Hypothesis Test for the Proportion<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 20.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=194><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>Null Hypothesis P =<o:p></o:p>
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0.27<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>Level of Significance<o:p></o:p>
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0.05<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>Number of Successes<o:p></o:p>
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9<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt" vAlign=bottom noWrap width=194>Sample Size<o:p></o:p>
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30<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=194><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 7"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>Sample Proportion<o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
0.30<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 316.15pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=422 colSpan=3>(computed from Successes / Sample Size)<o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 8"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=194><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 9"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>Z Test Statistic (Computed)<o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
0.37<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 10"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=194><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>
​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 11"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>
Direction of Test<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
Lower Crit Value<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
Upper Crit Value<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=73>
p-Value<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>
Decision<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 12"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=194><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73>
<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229>
<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 13"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>
Two-Tailed Test<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
-1.9600<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
1.9600<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=73>
0.7113<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>
Do not reject the null hypothesis<o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 14"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>
H1: P <> 0.27<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73>
<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229>
<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 15"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=194>
<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73>
<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229>
<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 16"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>
Upper-Tail Test<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
n/a<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=120>
1.6449<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=73>
0.3556<o:p></o:p>

​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>
Do not reject the null hypothesis<o:p></o:p>

​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 17"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=194>
H1: P > 0.27<o:p></o:p>​


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
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<o:p></o:p>

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<o:p></o:p>

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<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>
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<o:p></o:p>

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<o:p></o:p>

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Lower-Tail Test<o:p></o:p>

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-1.6449<o:p></o:p>

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n/a<o:p></o:p>

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0.6444<o:p></o:p>

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Do not reject the null hypothesis<o:p></o:p>

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H1: P < 0.27<o:p></o:p>​


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 21"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 145.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=194><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 90.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=120><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 54.45pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=73><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>
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If you REJECT the null hypothesis, conclude that H1 is true.<o:p></o:p>

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If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude that H1 is true.<o:p></o:p>

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NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).<o:p></o:p>​


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axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
I next wanted to know if the 27% success rate for making the playoffs translated to the population. The sample proportion is 30% since I used the number 88 as the trigger for post season play. I cannot reject any hypotheses but there is insufficient evidence to conclude that any alternative is true. This test yields no answer.
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 5.4pt; WIDTH: 552.15pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=736 border=0><TBODY><TR style="HEIGHT: 20.25pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 552.15pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 20.25pt" vAlign=bottom noWrap width=736 colSpan=8>Two Sample Hypothesis Test for the Mean (Independent Samples)<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext 1.0pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40><?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:eek:ffice:smarttags" /><st1:place w:st="on"><st1:State w:st="on">AL</st1:State></st1:place><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>NL<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 11.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=16 rowSpan=18><o:p></o:p>


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Level of Significance<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ffff99; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>0.05<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=80><o:p></o:p>


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 222.25pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=296 colSpan=2 rowSpan=7><o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>97<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>97<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=184><o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ffcc99; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80><st1:place w:st="on"><st1:State w:st="on">AL</st1:State></st1:place><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ffcc99; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>NL<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>96<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>88<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Sample Mean<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>83.000<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>79.188<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>95<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>88<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Sample Size<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>14<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>16<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>93<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>85<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Sample Standard Deviation<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>12.000<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>8.035<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 6"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>90<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>83<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Standard Error (Computed)<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>3.69<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=80 rowSpan=2><o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 7"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>89<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>82<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Test Statistic (Computed)<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>1.03<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 8"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>87<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>80<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=184 rowSpan=2><o:p></o:p>
<o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>Lower<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>Upper<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=68>p-Value<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>Decision<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 9"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>86<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>79<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>Crit Value<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>Crit Value<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 10"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>80<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>78<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Two-Tailed Test<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>-2.0484<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>2.0484<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=68>0.3098<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>Do not reject the null hypothesis<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 11"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>78<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>76<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>H1: (m1 <> m2)<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=80><o:p></o:p>


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=80><o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 12"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>78<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>76<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Upper-Tail Test<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>n/a<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>1.7011<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=68>0.1546<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>Do not reject the null hypothesis<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 13"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>70<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>76<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>H1: (m1 > m2 OR m2 < m1)<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=80><o:p></o:p>


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=80><o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 14"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>62<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>75<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>Lower-Tail Test<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>-1.7011<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=80>n/a<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=68>0.8454<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=229>Do not reject the null hypothesis<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 15"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40>61<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>71<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: #ccffff; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt" vAlign=bottom noWrap width=184>H1: (m1 < m2 OR m2 > m1)<o:p></o:p>



</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=80><o:p></o:p>


</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 60.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=80><o:p></o:p>

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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=68><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 171.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=229><o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 16"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>67<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=184>If you REJECT the null hypothesis, conclude H1 is true.<o:p></o:p>



</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 342.85pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=top noWrap width=457 colSpan=4 rowSpan=3><o:p></o:p>

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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 17"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40>66<o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=184>If you DO NOT REJECT the null hypothesis, there is insufficient evidence to conclude H1 is true.<o:p></o:p>


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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 18; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=40><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: yellow; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 29.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt" vAlign=bottom noWrap width=40><o:p></o:p>


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 138.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=184>NEVER conclude that the null hypothesis is true (i.e., we CANNOT ACCEPT the null).<o:p></o:p>



</TD></TR></TBODY></TABLE>
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
Last, I wanted to test the argument for the stronger league by win averages. I say both leagues are equal in strength, my null being population means are equal. I cannot reject any null hypothesis but there is insufficient evidence to conclude that any alternative is true. Although the sample means differed by nearly 4 wins, I cannot come to any conclusion with given data.
MULTIPLE REGRESSION MODEL ? MLB

<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 353.75pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=472 border=0><TBODY><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 206.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=275 colSpan=4>Multiple Regression Results<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=63><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 51.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=69><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 55.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=74><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 52.55pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=70><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=63><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=63><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67><o:p></o:p>

</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67><o:p></o:p>

</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 51.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=69><o:p></o:p>
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0<o:p></o:p>

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1<o:p></o:p>

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2<o:p></o:p>

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3<o:p></o:p>

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4<o:p></o:p>

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5<o:p></o:p>​


</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 51.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=69><o:p></o:p>

</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 55.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=74>Intercept<o:p></o:p>
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</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 52.55pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=70>
AVG<o:p></o:p>

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HR<o:p></o:p>

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SB<o:p></o:p>

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ERA<o:p></o:p>

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WHIP<o:p></o:p>​

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b<o:p></o:p>

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102.481<o:p></o:p>

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295.399<o:p></o:p>

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0.0861<o:p></o:p>

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0.0019<o:p></o:p>

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-62<o:p></o:p>

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108.984<o:p></o:p>

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0.0372<o:p></o:p>

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0.0301<o:p></o:p>

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4.7568<o:p></o:p>

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t<o:p></o:p>

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2.56609<o:p></o:p>

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2.71048<o:p></o:p>

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2.3163<o:p></o:p>

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0.0642<o:p></o:p>

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-2.5183<o:p></o:p>

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p-value<o:p></o:p>

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0.0170<o:p></o:p>

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0.0189<o:p></o:p>​


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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=63><o:p></o:p>

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<o:p></o:p>

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VIF<o:p></o:p>

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4.1038<o:p></o:p>

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4.3137<o:p></o:p>​


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<o:p></o:p>
My initial multiple regression model uses 5 subjectively important statistics in baseball. Since I?ve determined that the magic number to make the playoffs is 88 wins, I?d like to see if these key statistics somehow influence the goal of reaching the magic number. I consider AVG to be a measure of hitting proficiency while HR is indicative of power. SB data gauges speed. As with most offenses, the higher these numbers, the better. The defensive side of the ball requires lowers figures. The ERA tells me, that if a pitcher pitches all nine innings, the number of runs allowed and directly attributed to the pitcher. The WHIP indicates the number of runners, potential runs, allowed per inning using only hits and walks which are the sole responsibilities of the pitcher.

Predicted Wins<o:p></o:p>
= 102.481 + 295.399(AVG) + .0861(HR) + .0019(SB) + (-6.4908)(ERA) + (-62)(WHIP)<o:p></o:p>​

<o:p></o:p>
I use the p-value to determine contribution given other variables. With α = .05, I can eliminate SB and ERA from this model since the p-values > α. AVG, HR and WHIP are my contributing variables.
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
Adjusted Projected Wins

<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 256.5pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=342 border=0><TBODY><TR style="HEIGHT: 15.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 206.2pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 15.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=275 colSpan=4>Multiple Regression Results<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>
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0<o:p></o:p>​
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1<o:p></o:p>​
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2<o:p></o:p>​
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3<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 51.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=69> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 55.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=74>Intercept<o:p></o:p>
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AVG<o:p></o:p>​
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HR<o:p></o:p>​
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WHIP<o:p></o:p>​
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b<o:p></o:p>​
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118.765<o:p></o:p>​
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278.893<o:p></o:p>​
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0.0849<o:p></o:p>​
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-90.958<o:p></o:p>​
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s(b)<o:p></o:p>​
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37.1863<o:p></o:p>​
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107.846<o:p></o:p>​
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0.037<o:p></o:p>​
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12.245<o:p></o:p>​
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t<o:p></o:p>​
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3.19379<o:p></o:p>​
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2.58604<o:p></o:p>​
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2.2953<o:p></o:p>​
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-7.4282<o:p></o:p>​
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p-value<o:p></o:p>​
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0.0037<o:p></o:p>​
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0.0157<o:p></o:p>​
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0.0300<o:p></o:p>​
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0.0000<o:p></o:p>​
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 55.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=74><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 52.55pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=70><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=63><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 50.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67><o:p> </o:p>
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<o:p></o:p>​
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VIF<o:p></o:p>​
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1.0368<o:p></o:p>​
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1.0435<o:p></o:p>​
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1.0728<o:p></o:p>​
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<o:p> </o:p>
= 118.765 + 278.893(AVG) + .0849(HR) + (-90.958)(WHIP)<o:p></o:p>
Testing p-values again passes for contribution.
Now that I have my model, I?d like to consider some scenarios. First, can I expect an ?average? team to reach the magic number and the possibility of a playoff berth?
 
axp59

axp59

Jarhead
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Oct 8, 2008
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0
Taxachusetts
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 422.8pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=564 border=0><TBODY><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 142.55pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=190 colSpan=3>Prediction Interval<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 36.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=49><o:p> </o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 36.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=49><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=63><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 53.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=71>Given X<o:p></o:p>
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AVG<o:p></o:p>​
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HR<o:p></o:p>​
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WHIP<o:p></o:p>​
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</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 53.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=71> <o:p></o:p>
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1<o:p></o:p>​
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0.269<o:p></o:p>​
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180<o:p></o:p>​
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1.41<o:p></o:p>​
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</TD></TR><TR style="HEIGHT: 17.25pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 53.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=71> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 36.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=49><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 52.55pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=70><o:p> </o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 23pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=31><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 36.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=49><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=63><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=63><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 53.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=71> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 36.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=49>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 139.5pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=186 colSpan=3>(1-a) P.I. for Y for given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 23pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=31><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 36.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=49>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 133.9pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=179 colSpan=3>
(1-a) P.I. for E[Y | X]<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 53.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=71> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 36.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=49>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 52.55pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=70>
80.9667<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=63>10.664<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 23pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=31><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 36.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=49>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=63>
80.967<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 40pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 46.95pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=63>1.9153<o:p></o:p>
</TD></TR></TBODY></TABLE>
<o:p> </o:p>
An average season results in the figures above. The test concludes that for all teams achieving ?average? numbers in the three categories, they can expect to win 70 to 92 games. The prediction interval for an individual team is 79 to 83 wins. I can be 95% confident in these results.
Now I?d like to consider other scenarios. What if a team is best is one category but average in the two others?
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
Best Average:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 405pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=540 border=0><TBODY><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 126.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=169 colSpan=3>Prediction Interval<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67>Given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=65>
AVG<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
HR<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
WHIP<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37>
1<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=65>
0.287<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
180<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
1.41<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 17.25pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=65><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=37>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 128.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=171 colSpan=3>(1-a) P.I. for Y for given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 119.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=159 colSpan=3>
(1-a) P.I. for E[Y | X]<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=37>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=65>
85.9124<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>11.365<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
85.912<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>4.3729<o:p></o:p>
</TD></TR></TBODY></TABLE>
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
Best HR:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 405pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=540 border=0><TBODY><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 126.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=169 colSpan=3>Prediction Interval<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=65><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67>Given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=65>
AVG<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
HR<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
WHIP<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37>
1<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=65>
0.26927<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
236<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
1.41<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 17.25pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=65><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=37>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 128.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=171 colSpan=3>(1-a) P.I. for Y for given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 119.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=159 colSpan=3>
(1-a) P.I. for E[Y | X]<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=37>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=65>
85.7582<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>11.495<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
85.758<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>4.699<o:p></o:p>
</TD></TR></TBODY></TABLE>
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
Best WHIP:
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 405pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=540 border=0><TBODY><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 126.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=169 colSpan=3>Prediction Interval<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 1"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=65><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67>Given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=65>
AVG<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
HR<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
WHIP<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37>
1<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=65>
0.26927<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
180<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
1.27<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 17.25pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=65><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=37>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 128.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=171 colSpan=3>(1-a) P.I. for Y for given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 119.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=159 colSpan=3>
(1-a) P.I. for E[Y | X]<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=37>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=65>
93.5795<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>11.22<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
93.58<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>3.9812<o:p></o:p>
</TD></TR></TBODY></TABLE>
<o:p> </o:p>
This is absolutely startling! This just about confirms claims by many baseball ?experts? that pitching wins games. Now I?m curios what happens if it?s great pitching but very poor (lowest) hitting and power.
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
3,012
0
0
Taxachusetts
<TABLE class=MsoNormalTable style="MARGIN: auto auto auto 4.9pt; WIDTH: 405pt; BORDER-COLLAPSE: collapse; mso-padding-alt: 0in 5.4pt 0in 5.4pt" cellSpacing=0 cellPadding=0 width=540 border=0><TBODY><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 0; mso-yfti-firstrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 126.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=169 colSpan=3>Prediction Interval<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:eek:ffice:eek:ffice" /><o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53> <o:p></o:p>
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</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=65><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 2"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67>Given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=65>
AVG<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
HR<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
WHIP<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 12.75pt; mso-yfti-irow: 3"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37>
1<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=65>
0.255<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
124<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
1.27<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 12.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 17.25pt; mso-yfti-irow: 4"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=37><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=65><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 17.25pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 5"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=37>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 128.3pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=171 colSpan=3>(1-a) P.I. for Y for given X<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
1-a<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: black 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: windowtext 1pt solid; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 119.4pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-alt: solid windowtext .5pt" vAlign=bottom noWrap width=159 colSpan=3>
(1-a) P.I. for E[Y | X]<o:p></o:p>​
</TD></TR><TR style="HEIGHT: 13.5pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes"><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 50.1pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=67> <o:p></o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 27.6pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=37>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 48.7pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=65>
84.8883<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>12.721<o:p></o:p>
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: #ece9d8; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent" vAlign=bottom noWrap width=53><o:p> </o:p>
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; BACKGROUND: lime; PADDING-BOTTOM: 0in; BORDER-LEFT: windowtext 1pt solid; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt" vAlign=bottom noWrap width=53>
95%<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext 1.0pt; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
84.888<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: #ece9d8; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>
+ or -<o:p></o:p>​
</TD><TD style="BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0in; BORDER-LEFT: #ece9d8; WIDTH: 39.8pt; PADDING-TOP: 0in; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 13.5pt; BACKGROUND-COLOR: transparent; mso-border-top-alt: solid windowtext 1.0pt" vAlign=bottom noWrap width=53>7.1956<o:p></o:p>
</TD></TR></TBODY></TABLE>
<o:p> </o:p>
Well, at least I can comfortably believe that having great pitching is a good start. Strong pitching appears to make up for very poor power and hitting. Pitching alone makes this team competitive against average teams.
 
axp59

axp59

Jarhead
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Oct 8, 2008
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SUMMARY

There are 162 games in an MLB season. I can expect an average team to win 81 games. 81 wins will likely not get a team to the playoffs. A team should set their goal at winning 88 games. Winning at least 88 games will probably place the team in the top 27% of the league and a very good possibility of a playoff appearance.
Now that the goal is set, how does a team begin the journey to 88? It starts with pitching. Great pitching is enough to be competitive. Any improvements on power and hitting will propel a team above the ?average? teams. Assembling an average offensive team to go with the great pitching and a team can punch their ticket to the playoffs.
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
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There was one last piece but it was just raw data and can be found anywhere on the web. If one person finds this helpful, it has done its job. BOL
 
axp59

axp59

Jarhead
Forum Member
Oct 8, 2008
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Taxachusetts
#cruncher said:
Axp...have you ever used any of the things/models to try and predict the outcomes of the game(s) themselves?
Click to expand...

Not really. The closest would be the NBA where I do some statistical modeling but I think tracking how your numbers perform against the books is more important than the numbers the models yield themselves. IMHO
 
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