document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193657>Question 193657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The lifetime of a certain brand of battery is known to have a standard deviation of 10.5 hours. Suppose that a random sample of 120 such batteries has a mean lifetime of 40.9 hours. Based on this sample, find the 95% confidence interval for the true mean lifetime of all batteries of this brand.\r<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 #145353 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=145353\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The lifetime of a certain brand of battery is known to have a standard deviation of 10.5 hours. Suppose that a random sample of 120 such batteries has a mean lifetime of 40.9 hours. Based on this sample, find the 95% confidence interval for the true mean lifetime of all batteries of this brand. <BR>\n" );
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document.write( "x-bar = 40.9 hours  ;  s = 10.5<BR>\n" );
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document.write( "E = 1.96*10.5/sqrt(120) = 1.8787<BR>\n" );
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document.write( "95% C.I: 40.9 - 1.8787 < u < 40.9 + 1.8787<BR>\n" );
document.write( "95% C.I.: 39.02 < u < 42.78<BR>\n" );
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document.write( "Comment:  Some texts require you to use a t-distribution <BR>\n" );
document.write( "when calculating \"mean\" C.I.'s and working Hypothesis tests.<BR>\n" );
document.write( "If you use \"t\" to get your E value you get:<BR>\n" );
document.write( "95% C.I.: 39.002 < p < 42.798<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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