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 #700690 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=700690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Given Info:<BR>\n" );
document.write( "Confidence Level = C = 95% = 0.95<BR>\n" );
document.write( "sample size = n = 11<BR>\n" );
document.write( "sample standard deviation = s = 14.6\r<BR>\n" );
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document.write( "Based on the sample size, the degrees of freedom (df) is<BR>\n" );
document.write( "df = n-1 = 11-1 = 10\r<BR>\n" );
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document.write( "Let<BR>\n" );
document.write( "L = left chi-square critical value<BR>\n" );
document.write( "R = right chi-square critical value\r<BR>\n" );
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document.write( "We need to find the L & R values that make <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(L \le \chi^2 \le R) = 0.95\"> true. The symbol <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \chi^2\"> is the Chi-Square symbol\r<BR>\n" );
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document.write( "Using a table or calculator those approximate values are<BR>\n" );
document.write( "L = 3.247<BR>\n" );
document.write( "R = 20.483<BR>\n" );
document.write( "For this problem, I used a table. Specifically I used <a  rel=nofollow HREF=\"https://people.richland.edu/james/lecture/m170/tbl-chi.html\">this table</a>. Look at the df = 10 row. Highlight the columns that have 0.975 and 0.025 up top. These values are areas to the right of the values marked in the table. So for example, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(\chi^2 \ge 3.247) = 0.975\">. The middle area has 95% area. The two tails combine to 5% so each tail has area of 0.05/2 = 0.025\r<BR>\n" );
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document.write( "Now we can compute the confidence interval\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{\frac{(n-1)*s^2}{R}} \le \sigma \le \sqrt{\frac{(n-1)*s^2}{L}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{\frac{(11-1)*(14.6)^2}{20.483}} \le \sigma \le \sqrt{\frac{(11-1)*(14.6)^2}{3.247}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 10.2013130082227 \le \sigma \le 25.6219223966323\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 10.2 \le \sigma \le 25.6\"><BR>\n" );
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document.write( "The 95% confidence interval for the standard deviation is approximately <font color=red>(10.2, 25.6)</font><BR>\n" );
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