document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288027>Question 288027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At Oxnard University, a sample of 18 senior accounting majors showed a mean cumulative GPA of 3.35 with a standard deviation of 0.25. (a) At &#945; = .05 in a two-tailed test, does this differ significantly from 3.25 (the mean GPA for all business school seniors at the university)? (b) Use the sample to construct a 95 percent confidence interval for the mean. Does the confidence interval include 3.25? (c) Explain how the hypothesis test and confidence interval are equivalent. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208901 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=208901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At Oxnard University, a sample of 18 senior accounting majors showed a mean cumulative GPA of 3.35 with a standard deviation of 0.25. <BR>\n" );
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document.write( "(a) At &#945; = .05 in a two-tailed test, does this differ significantly from 3.25 (the mean GPA for all business school seniors at the university)?<BR>\n" );
document.write( "Ho: u = 3.25<BR>\n" );
document.write( "Ha: u is not equal to 3.25<BR>\n" );
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document.write( "Critical Values for 2-tail T-test with alpha = 5%:<BR>\n" );
document.write( "+-invT(0.975 with df = 17) =  +-2.1098<BR>\n" );
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document.write( "Test statistic: <BR>\n" );
document.write( "t(3.35) = (3.35-3.25)/[0.25/sqrt(18)] = 1.6971<BR>\n" );
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document.write( "Conclusion: Since the ts is not in either reject interval<BR>\n" );
document.write( "fail to reject Ho.  The mean for the 18 students did not<BR>\n" );
document.write( "differ significantly from 3.25<BR>\n" );
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document.write( " <BR>\n" );
document.write( "(b) Use the sample to construct a 95 percent confidence interval for the mean. Does the confidence interval include 3.25?<BR>\n" );
document.write( "sample mean: 3.35<BR>\n" );
document.write( "standard error: 2.1098*0.25/sqrt(18) = 0.1243<BR>\n" );
document.write( "95% CI: 3.35- 0.1243 < u < 3.35 + 0.1243<BR>\n" );
document.write( "95% CI: 3.2257 < u < 3.4743<BR>\n" );
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document.write( "(c) Explain how the hypothesis test and confidence interval are equivalent.<BR>\n" );
document.write( "The CI establishes 2.1098*0.25/sqrt(18) interval to the right and<BR>\n" );
document.write( "to the left of the sample mean.<BR>\n" );
document.write( "The hypothesis test establishes a 2.1098*0.25/sqrt(18) interval<BR>\n" );
document.write( "to the right and left of the hypothesized population mean.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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