document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80068>Question 80068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question 1\r<BR>\n" );
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document.write( "A.  A large public university want to estimate the average (mean) teaching experience of it's faculty. A preliminary random sample of 20 faculty yields a standard deviation of s=2.5 years. The dean wants to be 95% confident that the sample does not have a maximum error of estimate of more than 1.6 years. (Hint: this is maximum error of estimate E). How large of a sample should she use? Use the preliminary  sample standard deviation as an approximation of the population standard deviation. Round up to next whole number.\r<BR>\n" );
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document.write( "B. If she decides on a maximum error of 1.8 years and a level of significance of 95% how large of a sample should she use? Round up to next whole number.\r<BR>\n" );
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document.write( "Question 2\r<BR>\n" );
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document.write( "Suppose you are given a sample set of data consisting of 17 body temperatures, with s= 1.02. Assume that body temperatures are normally distributed. Find the 95% confidence interval for the population variance. Round off 2 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 #57443 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=57443\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Question 1 <BR>\n" );
document.write( "A. A large public university want to estimate the average (mean) teaching experience of it's faculty. A preliminary random sample of 20 faculty yields a standard deviation of s=2.5 years. The dean wants to be 95% confident that the sample does not have a maximum error of estimate of more than 1.6 years. (Hint: this is maximum error of estimate E). How large of a sample should she use? Use the preliminary sample standard deviation as an approximation of the population standard deviation. Round up to next whole number.<BR>\n" );
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document.write( "E=z*(sigma/sqrt(n))<BR>\n" );
document.write( "sqrt(n)=z*sigma/E<BR>\n" );
document.write( "Your problem:<BR>\n" );
document.write( "sqrt(n)=1.96[2.5]/1.6<BR>\n" );
document.write( "sqrt(n)=3.0625<BR>\n" );
document.write( "n=9.4<BR>\n" );
document.write( "Rounding up gives n=10<BR>\n" );
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document.write( "B. If she decides on a maximum error of 1.8 years and a level of significance of 95% how large of a sample should she use? Round up to next whole number.<BR>\n" );
document.write( "sqrt(n)=1.96[2.5]/1.8<BR>\n" );
document.write( "sqrtr(n)= 2.72222<BR>\n" );
document.write( "n=7.7<BR>\n" );
document.write( "Rounding gives n=8<BR>\n" );
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document.write( "Question 2 <BR>\n" );
document.write( "Suppose you are given a sample set of data consisting of 17 body temperatures, with s= 1.02. Assume that body temperatures are normally distributed. Find the 95% confidence interval for the population variance. Round off 2 decimal places.<BR>\n" );
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document.write( "[(n-1)s^2/X(r)]< sigma^2 < [(n-1)s^2/X(l)]<BR>\n" );
document.write( "[(17-1)1.02^2/28.845] < sigma^2 < [(17-1)1.02^2/6.90766<BR>\n" );
document.write( "0.5771 < sigma^2 <2.4098<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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