document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134328>Question 1134328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You wish to test the following claim (Ha) at a significance level of α=0.05. For the context of this problem ,μd = μ2 − μ1 where the first data set represents a pre-test and the second data set represents a post-test.\r<BR>\n" );
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document.write( "Ho:μd=0<BR>\n" );
document.write( "Ha:μd>0\r<BR>\n" );
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document.write( "You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=19 subjects. The average difference (post - pre) is d=5 (Note: d has a horizontal bar over it) with a standard deviation of the differences of sd=10.4.\r<BR>\n" );
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document.write( "1. What is the critical value for this test? (Report answer accurate to three decimal places.) <BR>\n" );
document.write( "critical value = \r<BR>\n" );
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document.write( "2. What is the test statistic for this sample? (Report answer accurate to three decimal places.) <BR>\n" );
document.write( "test statistic = \r<BR>\n" );
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document.write( "3. The test statistic is...<BR>\n" );
document.write( "(a) in the critical region<BR>\n" );
document.write( "(b) not in the critical region\r<BR>\n" );
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document.write( "4. This test statistic leads to a decision to...<BR>\n" );
document.write( "(a) reject the null<BR>\n" );
document.write( "(b) accept the null<BR>\n" );
document.write( "(c) fail to reject the null\r<BR>\n" );
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document.write( "5. As such, the final conclusion is that...<BR>\n" );
document.write( "(a) There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.\r<BR>\n" );
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document.write( "(b) There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.\r<BR>\n" );
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document.write( "(c) The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.\r<BR>\n" );
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document.write( "(d)There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.\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 #751793 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=751793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a paired t-test with tdf=18,0.95, upper tail probability, value of t being 1.734<BR>\n" );
document.write( "and the test statistic is t=5/10.4/sqrt(19), which is 2.096, in the critical region. (t>1.734)<BR>\n" );
document.write( "reject Ho with p-value 0.0252<BR>\n" );
document.write( "c<BR>\n" );
document.write( "Ho is claiming that the mean difference is 0 (or less than 0).<BR>\n" );
document.write( "Ha is claiming that the mean difference is greater than 0.<BR>\n" );
document.write( "We reject Ho (that the mean difference is <=0) and conclude that the mean difference is >0.<BR>\n" );
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