document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085767>Question 1085767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need to find the test statisctic. <BR>\n" );
document.write( "Please check the chart in the image: http://imgur.com/a/IUiNM </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699859 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what are you comparing?  means or variances?<BR>\n" );
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document.write( "student states the following<BR>\n" );
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document.write( "The sample covariance between the mid-term and final exam grades is given as 68.9. I need to test the null hypothesis that the within-student average grades for the mid-term and final exams are the same against a one-sided alternative that the within-student average grade for the final exam is lower than the average grade for the mid-term exam. <BR>\n" );
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document.write( "The sample covariance between the mid-term and final exam grades is given as 68.9<BR>\n" );
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document.write( "This means the final exam grade increases as the mid-term exam grade increases <BR>\n" );
document.write( "because the sample covariance is greater than zero.<BR>\n" );
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document.write( "Ho:  mid-term average = final grade average<BR>\n" );
document.write( "H1:  mid-term average > final grade average<BR>\n" );
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document.write( "Standard Error(SE) = square root[(s1^2/n1) + (s2^2/n2)]<BR>\n" );
document.write( "SE = square root[(14.4^2/176) + (14.5^2/176)] = 1.5404<BR>\n" );
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document.write( "Degrees of Freedom (DF) = (s1^2/n1 + s2^2/n2)^2 / { [ (s1^2/ n1)^2 / (n1 - 1) ] + [ (s2^2 / n2)^2 / (n2 - 1) ] }<BR>\n" );
document.write( "DF = (14.4^2/176 + 14.5^2/176)^2 / {[(14.4^2/176)^2 / 175] + [(14.5^2/176)^2 / 175]} = 349.98 approx 350<BR>\n" );
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document.write( "t statistic = (x1 - x2) / SE = (72.5 - 68.2) /  1.5404 = 2.79<BR>\n" );
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document.write( "Probability ( t < or = 2.79) is 0.9972<BR>\n" );
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document.write( "Since the P-value (0.9972) is greater than the significance level (0.05), we cannot reject the null hypothesis.<BR>\n" );
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