document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052861>Question 1052861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this:\r<BR>\n" );
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document.write( "In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words.<BR>\n" );
document.write( "Each was asked to list as many of the words as he or she could remember both 1 hour and 24<BR>\n" );
document.write( "hours later. The result is shown in the following table.\r<BR>\n" );
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document.write( "                              Number of Words Recalled\r<BR>\n" );
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document.write( "Subject   _________ 1 hour later    _________                24 hours later<BR>\n" );
document.write( "1 _________          14                _________              12<BR>\n" );
document.write( "2  _________         18                    _________          15<BR>\n" );
document.write( "3  _________         11                 _________             9<BR>\n" );
document.write( "4  _________         13                   _________           12<BR>\n" );
document.write( "5  _________         12                   _________           12\r<BR>\n" );
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document.write( "Is there evidence to suggest that the mean number of words recalled after 24 hours are less<BR>\n" );
document.write( "than the mean recall after 1 hour? \r<BR>\n" );
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document.write( "Assume we want to use a 0.05 significance level to test the claim. Please show all work.\r<BR>\n" );
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document.write( "(a) Identify the null hypothesis and the alternative hypothesis.\r<BR>\n" );
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document.write( "(b) Determine the test statistic.\r<BR>\n" );
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document.write( "(c) Determine the P-value for this test.\r<BR>\n" );
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document.write( "(d) Is there sufficient evidence to support the claim that the mean number of words recalled after 24 hours is less than the mean recall after 1 hour? Justify your conclusion.\r<BR>\n" );
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document.write( "Thank you very much for any help!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668164 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=668164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: the number of words recalled is unchanged or greater<BR>\n" );
document.write( "Ha: the number of words recalled is less.<BR>\n" );
document.write( "alpha=0.05, one way test<BR>\n" );
document.write( "Paired t-test<BR>\n" );
document.write( "4 degrees of freedom<BR>\n" );
document.write( "Critical value is -2.132 <BR>\n" );
document.write( "difference defined here as number after 24 hours-number after 12 hours.<BR>\n" );
document.write( "average d/[s/sqrt(n)]<BR>\n" );
document.write( "This is -1.6/(1.14/sqrt(5))<BR>\n" );
document.write( "That is t=-3.14<BR>\n" );
document.write( "This has a p-value of 0.0175, and we can conclude that there is a significant difference (reject Ho).<BR>\n" );
document.write( "The important part of this problem is to use each person as their own control.  The df are less, but the variability is much less.\r<BR>\n" );
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