document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129839>Question 129839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How tall are college hockey players?  The average height has been 68.3 inches.  A random sample of 14 hockey players gave a mean height of 69.1 inches.  We may assume that x has a normal distribution with &#963; = 0.9 inch.  Does this indicate that the population mean height is different from 68.3 inches?  Use 5% level of significance.\r<BR>\n" );
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document.write( "a) State the null and the alternate hypothesis.<BR>\n" );
document.write( "b) Identify the sampling distribution to be used:  the standard normal distribution or the Student's t distribution. Find the critical value(s).<BR>\n" );
document.write( "c) Compute the z or t value of the sample test statistic.<BR>\n" );
document.write( "d) Find the P value or an interval containing the P value for the sample test statistic.<BR>\n" );
document.write( "e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level.  Explain your conclusion in the context of the problem.<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 #94804 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=94804\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How tall are college hockey players? The average height has been 68.3 inches. A random sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with &#963; = 0.9 inch. Does this indicate that the population mean height is different from 68.3 inches? Use 5% level of significance. <BR>\n" );
document.write( "a) State the null and the alternate hypothesis.<BR>\n" );
document.write( "Ho: mu = 68.3<BR>\n" );
document.write( "Ha: mu is not equal to 68.3 (2-tailed test)<BR>\n" );
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document.write( "b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical value(s).<BR>\n" );
document.write( "t-distribution; Critical value = +-1.96 for alpha = 5% on two-tail test.<BR>\n" );
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document.write( "c) Compute the z or t value of the sample test statistic.<BR>\n" );
document.write( "t(69.1) = (69.1-68.3)/[0.9/sqrt(14)] = 0.8*sqrt(14)/0.9 = 3.3259...<BR>\n" );
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document.write( "d) Find the P value or an interval containing the P value for the sample test statistic.<BR>\n" );
document.write( "p-value = 2*P(3.3259<t<10 for df=13) = 2*0.0184..= 0.0368426<BR>\n" );
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document.write( "e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level. Explain your conclusion in the context of the problem.<BR>\n" );
document.write( "Since p-value is less than 5% and since the test statistic is in the <BR>\n" );
document.write( "rejection region we Reject Ho.  The test indicates there is significant<BR>\n" );
document.write( "statistical evidence that the mean height of hockey players is not 68.3.<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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