document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=730068>Question 730068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The president of a large university wishes to estimate the average age of the students presently enrolled. From past studies, the standard deviation &#963; is known to be 2 years. A sample of 50 students is selected and the mean is found to be 23.3 years.<BR>\n" );
document.write( " a. Find the 99% confidence interval of the population.<BR>\n" );
document.write( " b. Find the 99% confidence interval for the population standard deviation<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 #446451 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=446451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first part to get you started\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "I'm assuming you want the 99% confidence interval of the population mean. Let me know if it's some other variable.\r<BR>\n" );
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document.write( "The sample mean is 23.3\r<BR>\n" );
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document.write( "The margin of error is\r<BR>\n" );
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document.write( "E = z*sigma/sqrt(n)\r<BR>\n" );
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document.write( "E = 2.576*sigma/sqrt(n) ... use a calculator to find the critical value for z (let me know if you need me to show you how to do this on a calculator)\r<BR>\n" );
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document.write( "E = 2.576*2/sqrt(50) ... plug in the other given values\r<BR>\n" );
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document.write( "E = 0.72860282733461\r<BR>\n" );
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document.write( "The lower bound of the confidence interval is \r<BR>\n" );
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document.write( "L = xbar - E\r<BR>\n" );
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document.write( "L = 23.3 - 0.72860282733461\r<BR>\n" );
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document.write( "L = 22.5713971726653\r<BR>\n" );
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document.write( "The upper bound of the confidence interval is \r<BR>\n" );
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document.write( "L = xbar + E\r<BR>\n" );
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document.write( "L = 23.3 + 0.72860282733461\r<BR>\n" );
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document.write( "L = 24.0286028273347\r<BR>\n" );
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document.write( "So the 99% confidence interval for the population mean is \r<BR>\n" );
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document.write( "(L, U) = (22.5713971726653, 24.0286028273347)\r<BR>\n" );
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