document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1058636>Question 1058636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following data were randomly drawn from an approximately normal population.<BR>\n" );
document.write( "2, 6, 11, 12, 21, 23\r<BR>\n" );
document.write( "\n" );
document.write( "use these data, find a 95% confidence interval for the population standard deviation. Then complete the table below.\r<BR>\n" );
document.write( "\n" );
document.write( "Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. \r<BR>\n" );
document.write( "\n" );
document.write( "what is the lower limit of the 95% confident interval and what is the upper limit of the 95% confident interval </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #673740 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=673740\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since we are trying to estimate the standard deviation in the population, we choose the standard deviation as the sample statistic.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Sample mean is (2 + 6 + 11 + 12 + 21 + 23) / 6 = 12.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Sample standard deviation is square root( (1/6) * summation from 1 to 6 (x(i) - sample mean)^2 ) = 8.2158<BR>\n" );
document.write( ":<BR>\n" );
document.write( "degrees of freedom(df) = 6 - 1 = 5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "alpha(a) = 1 - (95/100) = 0.005<BR>\n" );
document.write( ":<BR>\n" );
document.write( "critical probability(p*) = 1 - (a/2) = 0.975<BR>\n" );
document.write( ":<BR>\n" );
document.write( "we use the chi-square table to find two values<BR>\n" );
document.write( ":<BR>\n" );
document.write( "x^2 (1 - (a/2) ) and 5 degrees of freedom = 0.831<BR>\n" );
document.write( "x^2(a/2) and five degrees of freedom = 12.833<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the 95% confidence interval for the variance is<BR>\n" );
document.write( ":<BR>\n" );
document.write( "5*(8.2158)^2/12.833 < variance < 5*(8.2158)^2/0.831<BR>\n" );
document.write( ":<BR>\n" );
document.write( "26.2991 < variance < 406.1334<BR>\n" );
document.write( ":<BR>\n" );
document.write( "standard deviation = square root of the variance<BR>\n" );
document.write( ":<BR>\n" );
document.write( "*************************************************************<BR>\n" );
document.write( "95% confidence interval for the population standard deviation<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(5.1283, 20.1528)<BR>\n" );
document.write( "*************************************************************<BR>\n" );
document.write( ":<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );