document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190015>Question 1190015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	You manage a bookstore. Your competitor claims that the average textbook at their bookstore costs less than $100. You want to test this claim. You randomly sample 40 books and get the average cost of $95 and the sample standard deviation of this sample to be $20.\r<BR>\n" );
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document.write( "a.	Run the hypothesis test at the standard alpha level of 5% and copy and paste the results below. Make sure you show the Ho, Ha, critical value, test statistic, p-values and decision.\r<BR>\n" );
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document.write( "b.	Summarize your results at the 0.05 alpha level significance level.\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 #821604 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=821604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Ho: mu >= 100<BR>\n" );
document.write( "Ha: mu < 100<BR>\n" );
document.write( "This is a left-tailed test because of the inequality sign in the alternative hypothesis.<BR>\n" );
document.write( "The rejection region is to the left of the critical value.\r<BR>\n" );
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document.write( "n = 40 = sample size<BR>\n" );
document.write( "n > 30 so we can use the Z distribution here\r<BR>\n" );
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document.write( "Given info:<BR>\n" );
document.write( "mu = 100 is what we assume is the case<BR>\n" );
document.write( "xbar = sample mean = 95<BR>\n" );
document.write( "s = sample standard deviation = 20\r<BR>\n" );
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document.write( "Test Statistic:<BR>\n" );
document.write( "z = (xbar - mu)/(s/sqrt(n))<BR>\n" );
document.write( "z = (95 - 100)/(20/sqrt(40))<BR>\n" );
document.write( "z = -1.58<BR>\n" );
document.write( "The value is approximate\r<BR>\n" );
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document.write( "Use a Z table or calculator to find that<BR>\n" );
document.write( "P(Z < -1.58) = 0.05705<BR>\n" );
document.write( "This is the approximate p-value\r<BR>\n" );
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document.write( "The p-value is not less than alpha = 0.05, so we fail to reject the null. <BR>\n" );
document.write( "In other words, we don't have enough info to overturn the null. <BR>\n" );
document.write( "The null was that mu >= 100, so either mu = 100 or mu > 100. <BR>\n" );
document.write( "We can interpret this as \"The average textbook is $100 or more\", or something along those lines.\r<BR>\n" );
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document.write( "If you were to use a table or calculator, you should find that the z critical value is roughly -1.645 when considering a left-tailed test.<BR>\n" );
document.write( "Effectively,<BR>\n" );
document.write( "P(Z < -1.645) = 0.05 approximately\r<BR>\n" );
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document.write( "Compare the test statistic (-1.58) and the critical value (-1.645)<BR>\n" );
document.write( "The test statistic is not to the left of the critical value, so the test statistic is not in the rejection region. \r<BR>\n" );
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document.write( "--------------------------------------------<BR>\n" );
document.write( "Summary:\r<BR>\n" );
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document.write( "Test Statistic: z = -1.58<BR>\n" );
document.write( "critical value: z = -1.645<BR>\n" );
document.write( "P-value = 0.05705<BR>\n" );
document.write( "Decision: Fail to reject the null<BR>\n" );
document.write( "Interpretation: The average textbook is $100 or more\r<BR>\n" );
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