document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201399>Question 1201399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lifetimes of AAA batteries are approximately normally distributed. A manufacturer wants to estimate the standard deviation of the lifetime of the AAA batteries it produces. A random sample of 15 AAA batteries produced by this manufacturer lasted a mean of 9.5 hours with a standard deviation of 1.7 hours. Find a 95% confidence interval for the population standard deviation of the lifetimes of AAA batteries produced by the manufacturer. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835787 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample mean is 9.5 hours.<BR>\n" );
document.write( "sample standard devition is 1.7 hours.<BR>\n" );
document.write( "sample size is 15.<BR>\n" );
document.write( "t-score is indicated because the standard deviation is taken from the sample rather than the population.<BR>\n" );
document.write( "since you are looking at the mean of a sample of several elements, you would use the standard error rather than the standard deviation.<BR>\n" );
document.write( "standard error = standard deviation / sqrt(sample size) = 1.7 / sqrt(15) = .4389381126.<BR>\n" );
document.write( "t-score formula is t = (x - m) / s<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is the upper or lower limit of the 95% considence interval.<BR>\n" );
document.write( "m is mean of the sample.<BR>\n" );
document.write( "s is the standard error.<BR>\n" );
document.write( "the 95% confidence interval t-tscore with 14 degrees of freedom is plus or minus 2.144786681.<BR>\n" );
document.write( "for the upper limit of the confidence interval, the t-score formula becomes:<BR>\n" );
document.write( "2.144786681 = (x - 9.5) / .4389381126 <BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 2.144786681 * .4389381126 + 9.5 = 10.44142862.<BR>\n" );
document.write( "for the lower limit of the confidence interval, the t-score formula becomes:<BR>\n" );
document.write( "-2.144786681 = (x - 9.5) / .4389381126 <BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = -2.144786681 * .4389381126 + 9.5 = 8.558571382.<BR>\n" );
document.write( "your 95% confidence interval is 8.558571382 to 10.44142862.<BR>\n" );
document.write( "round to two decimal places to get:<BR>\n" );
document.write( "your 95% confidence interval is 8.56 to 10.44. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );