document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269290>Question 269290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of 51 observations was selected from a normally distributed population. The sample mean was xbar = 64, and the sample variance was s2 = 48.0. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 9 at the 0.02 level of significance?  Use the p-value method.<BR>\n" );
document.write( "·         State the null and alternate hypotheses<BR>\n" );
document.write( "·         Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "·         Determine the corresponding probability, and compare to<BR>\n" );
document.write( "·         State your decision: Should the null hypothesis be rejected? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197396 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=197396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A random sample of 51 observations was selected from a normally distributed population. <BR>\n" );
document.write( "The sample mean was xbar = 64, and the sample variance was s2 = 48.0. <BR>\n" );
document.write( "Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 9 at the 0.02 level of significance? <BR>\n" );
document.write( "Use the p-value method.<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "· State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: sigma^2 = 81<BR>\n" );
document.write( "H1: sigma^2 is not equal to 81<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "· Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "Chi-Sq = (51-1)48/81 = 29.04<BR>\n" );
document.write( "------<BR>\n" );
document.write( "· Determine the corresponding probability, and compare to ?<BR>\n" );
document.write( "p-value = 2P(Chi-sq > 29.04 with df = 50) is approximately 2(0.005)= 0.01<BR>\n" );
document.write( "Note: I don't have technology that will so me the exact p-value.<BR>\n" );
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document.write( "· State your decision: Should the null hypothesis be rejected?<BR>\n" );
document.write( "Since my p-value is less than 2%, I would reject Ho.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "sigma^2 is not 81, so sigma is not 9<BR>\n" );
document.write( "=========================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );