document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131798>Question 1131798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A simple random sample from a population with a normal distribution of 106 body temperatures has x =98.90 degrees and s =0.61 degrees. Construct a 95&#8203;% confidence interval estimate of the standard deviation of body temperature of all healthy humans.<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 #748527 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748527\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size(n) is 106 body temperatures<BR>\n" );
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document.write( "degrees of freedom = 106 - 1 = 105<BR>\n" );
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document.write( "the mean of the sample is 98.90<BR>\n" );
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document.write( "standard deviation of the sample is 0.61<BR>\n" );
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document.write( "We use the chi-square distribution to construct the 95% confidence interval(CI) for the population standard deviation<BR>\n" );
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document.write( "alpha(a) = 1 -(95/100) = 0.05<BR>\n" );
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document.write( "critical probability(p*) = 1 -(a/2) = 0.975<BR>\n" );
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document.write( "chi-square(0.975) = 78.536<BR>\n" );
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document.write( "chi-square(0.025) = 135.247<BR>\n" );
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document.write( "population variance(0.975) = ((106-1)*(0.61)^2)/78.536 = 0.4975<BR>\n" );
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document.write( "population variance(0.025) = ((106-1)*(0.61)^2)/135.247 = 0.2889<BR>\n" );
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document.write( "take the square roots to get standard deviation<BR>\n" );
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document.write( "the 95% confidence interval is (0.5375, 0.7053)<BR>\n" );
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