document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250039>Question 250039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> . A random sample of 41 observations was selected from a normally distributed population. The sample mean was x = 61, and the sample variance was s^2 = 18.0. Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 4 at the 0.05 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 a<BR>\n" );
document.write( "·         State your decision: Should the null hypothesis be rejected?\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #182182 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=182182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A random sample of 41 observations was selected from a normally distributed population. <BR>\n" );
document.write( "The sample mean was x = 61, and the sample variance was s^2 = 18.0. <BR>\n" );
document.write( "Does the sample show sufficient reason to conclude that the population standard deviation is not equal to 4 at the 0.05 level of significance? <BR>\n" );
document.write( "Use the p-value method.<BR>\n" );
document.write( "· State the null and alternate hypotheses<BR>\n" );
document.write( "Ho: sigma = 4<BR>\n" );
document.write( "H1: sigma is not equal to 4<BR>\n" );
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document.write( "· Determine which test statistic applies, and calculate it<BR>\n" );
document.write( "Chi-Sq = (n-1)s^2/sigma^2 = 40*18/16 = 45<BR>\n" );
document.write( "· Determine the corresponding probability, and compare to a ?????<BR>\n" );
document.write( "left-tail critical value:24.433 <BR>\n" );
document.write( "right-tail critical value: 59.342<BR>\n" );
document.write( "· State your decision: Should the null hypothesis be rejected?<BR>\n" );
document.write( "The test stat is in the fail to reject interval.<BR>\n" );
document.write( "Ho should not be rejected.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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