document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=458331>Question 458331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:<BR>\n" );
document.write( "0	260	356	403	536	0	268	369	428	536<BR>\n" );
document.write( "268	396	469	536	162	338	403	536	536	130<BR>\n" );
document.write( "(a)	Construct a 95 percent confidence interval for the true mean.<BR>\n" );
document.write( "(b)	Why might normality be an issue here?<BR>\n" );
document.write( "(c)	What sample size would be needed to obtain an error of ± 10 square millimeters with 99 percent confidence?<BR>\n" );
document.write( "(d)	If this is not a reasonable requirement, suggest one that is. (Data are from a project by MBA student Daniel R. Dalach.)<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 #314599 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=314599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sample of 20 pages was taken without replacement fromthe 1,591-page phone directory Ameritech Pages Plus Yellow pages<BR>\n" );
document.write( "On each page, the mean area devoted to display ads was measured (a display as is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below: <BR>\n" );
document.write( "0; 260; 356; 403; 536; 0; 268; 369; 428; 536; 268; <BR>\n" );
document.write( "396; 469; 536; 162; 338; 403; 536; 536; 130<BR>\n" );
document.write( "----------------------------- <BR>\n" );
document.write( "a) construct a 95% confidence interval for the true mean<BR>\n" );
document.write( "x-bar = 346.5<BR>\n" );
document.write( "E = t*s/sqrt(n)<BR>\n" );
document.write( "E = 2.093=79.738<BR>\n" );
document.write( "95% CI: 346.5-79.738 < u < 346.5+79.738<BR>\n" );
document.write( "95% CI: 266.762 < u < 426.24<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "b Why might normallity be an issue here?<BR>\n" );
document.write( "All the pages were taken from the same phone book.\r<BR>\n" );
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document.write( "The CI is a statement about the whole population of phone books.<BR>\n" );
document.write( "The sample might very well not be representative of the whole population.<BR>\n" );
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document.write( "c. What sample size would be needed to obtain an error of _+ 10 square millimeters with 99% confidence<BR>\n" );
document.write( "Since E = t*s/(sqrt(n))<BR>\n" );
document.write( "sqrt(n) = t*s/E<BR>\n" );
document.write( "n = [t*s/E]^2 = [2.093*170.378/10]^2 = 1271.64<BR>\n" );
document.write( "Rounded up you get n=1272<BR>\n" );
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document.write( "d. If this is not a reasonable requirement, suggest one that is.<BR>\n" );
document.write( "You could lessen the sample size by decreasing the confidence<BR>\n" );
document.write( "or increasing the error limit.<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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