document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620853>Question 620853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two methods of memorizing difficult material are being tested to determine if one produces better retention. A random sample of 7 pairs of students matched according to I.Q. and academic background are included in the study. Method A is randomly assigned to one student in each pair. The scores on a memorization test are listed below (by percent). Using a = .05, is there evidence to conclude a significant difference between the effectiveness of the two methods?<BR>\n" );
document.write( "t – test: Paired Sample for Mean	Method A	Method B<BR>\n" );
document.write( "Mean	61.86	65.43<BR>\n" );
document.write( "Variance	70.4762	170.2857<BR>\n" );
document.write( "Observations	7	7<BR>\n" );
document.write( "t statistic	-1.622	<BR>\n" );
document.write( "P-value one-tail	0.078	<BR>\n" );
document.write( "t Critical value one-tail	1.943	<BR>\n" );
document.write( "P-value two-tail	0.156	<BR>\n" );
document.write( "t Critical value two-tail	2.447	\r<BR>\n" );
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document.write( "Is there evidence of a difference between the effectiveness of the two methods?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #567483 by </B><A HREF=/tutors/aboutme.mpl?userid=Cupjohn><B>Cupjohn(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cupjohn><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=567483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a matched pair t -test.<BR>\n" );
document.write( "So d\"bar\" is 61.86-65.43 = -3.57<BR>\n" );
document.write( "the standard deviation is sqrt(70.4762+170.2857)=15.52<BR>\n" );
document.write( "n = 7\r<BR>\n" );
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document.write( "So the t test statistic is -3.57/(15.52/sqrt(7))=-0.608591\r<BR>\n" );
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document.write( "Ho = \"mu\"d = 0<BR>\n" );
document.write( "H1 = \"mu\"d is not = 0\r<BR>\n" );
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document.write( "test statistic is less than the critical values so we cannot reject the null, thus there is no evidence of a difference between the two methods </SPAN>\n" );
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