document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967336>Question 967336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4.  The IRS claims that it takes 87 minutes to prepare a tax form.  You believe it takes longer than 87 minutes.  You ask 19 tax filers and find the following preparation times:<BR>\n" );
document.write( "61, 74, 78, 79, 87, 88, 96, 97, 98, 98, 99, 100, 100, 101, 108, 110, 117, 120, 121<BR>\n" );
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document.write( "Determine if the preparation time is significantly longer than 87 minutes.  Use  &#945;  = .025.<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 #591259 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=591259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "mu = 87 (based on the null hypothesis below)<BR>\n" );
document.write( "n = 19<BR>\n" );
document.write( "alpha = 0.025\r<BR>\n" );
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document.write( "Use a calculator to compute the following:<BR>\n" );
document.write( "sample mean: xbar = 96.421<BR>\n" );
document.write( "sample standard deviation: s = 15.848\r<BR>\n" );
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document.write( "Hypothesis:<BR>\n" );
document.write( "H0: mu = 87<BR>\n" );
document.write( "H1: mu > 87\r<BR>\n" );
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document.write( "Test Statistic:\r<BR>\n" );
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document.write( "t = (xbar - mu)/(s/sqrt(n))<BR>\n" );
document.write( "t = (96.421 - 87)/(15.848/sqrt(19))<BR>\n" );
document.write( "t = 2.591\r<BR>\n" );
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document.write( "Now use a calculator to compute the area under the curve to the right of t = 2.591\r<BR>\n" );
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document.write( "According to <a  rel=nofollow HREF=\"http://stattrek.com/online-calculator/t-distribution.aspx\">this calculator</a>, we find that P(T < 2.591) = 0.9908 (note: degrees of freedom = n-1 = 19-1 = 18)\r<BR>\n" );
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document.write( "So this means\r<BR>\n" );
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document.write( "P(T > 2.591) = 1 - P(T < 2.591)<BR>\n" );
document.write( "P(T > 2.591) = 1 - 0.9908<BR>\n" );
document.write( "P(T > 2.591) = 0.0092\r<BR>\n" );
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document.write( "This is the p-value.\r<BR>\n" );
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document.write( "p-value = 0.0092\r<BR>\n" );
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document.write( "Since the p-value (0.0092) is smaller than the value of alpha (0.025), this means we reject the null hypothesis H0.\r<BR>\n" );
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document.write( "So we must conclude that the alternative hypothesis H1: mu > 87 is true.\r<BR>\n" );
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document.write( "Therefore, we conclude that the average times takes significantly longer than 87 minutes. </SPAN>\n" );
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