document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086484>Question 1086484</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 11 pipes has a standard deviation of 14.6 inches. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700689 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=700689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We use a chi-squared distribution which gives us a confidence interval that is not symmetric about the sample standard deviation<BR>\n" );
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document.write( "We assume that the population of pipes is normally distributed, then<BR>\n" );
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document.write( "chi-squared(1 - a/2) < or = (n-1)s^2/(std. dev.)^2 < or = chi-squared(a/2)<BR>\n" );
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document.write( "where a is the alpha, s is the sample standard deviation, and std. dev. is the population standard deviation<BR>\n" );
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document.write( "a = (1 - 95/100) = 0.05<BR>\n" );
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document.write( "for this problem a = 0.05, degrees of freedom = 11 - 1 = 10, then<BR>\n" );
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document.write( "chi-squared(0.975) = 20.5 and chi-squared(0.025) = 3.25<BR>\n" );
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document.write( "we evaluate (n-1)s^2 / chi-squared for 20.5 and 3.25<BR>\n" );
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document.write( "(11-1) * 14.6^2 / 20.5 = 103.98<BR>\n" );
document.write( "(11-1) * 14.6^2 / 3.25 = 655.88<BR>\n" );
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document.write( "we take the square root of 103.98 and 655.88<BR>\n" );
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document.write( "square root(103.98) = 10.197 approx 10.2<BR>\n" );
document.write( "square root(655.88) = 25.610 approx 25.6<BR>\n" );
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document.write( "the 95% confidence interval is (10.2, 25.6)<BR>\n" );
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