document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145004>Question 145004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sample of 20 pages was taken without replacement from 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 multi colored 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\r<BR>\n" );
document.write( "\n" );
document.write( "a. construct a 95 percent confidence interval for the tru mean. b) why might normality be an issue here? c). what sample size would be needed to obtain an error of +/- 10 square millimeters with 99 percent confidence? d). if this is not a reasonable requirement, suggest one that is. (data from a project by MBA student Daniel R. Dalach.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #105708 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=105708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sample of 20 pages was taken without replacement from the 1,591-page phone directory<BR>\n" );
document.write( "Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured<BR>\n" );
document.write( "(a display ad is a large block of multicolored illustrations, maps, and text). The data (in<BR>\n" );
document.write( "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( "x-bar = 346.5<BR>\n" );
document.write( "s = 170.378<BR>\n" );
document.write( "t-critical value for 95% CI with df=19 = 2.093<BR>\n" );
document.write( "E = 2.093*170.378/sqrt(20) = 2.0931.96*38.0976=79.74<BR>\n" );
document.write( "95% CI : (346.5-79.74,346.5+79.74)<BR>\n" );
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document.write( "(b) Why might normality be an issue here<BR>\n" );
document.write( "The CI is a statement about the whole population. The random<BR>\n" );
document.write( "sample is probably not 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 percent confidence?<BR>\n" );
document.write( "n = [t*s/E] <BR>\n" );
document.write( "n = [2.093*170.378/10]^2 = 1271.64<BR>\n" );
document.write( "n = 1272 (when rounded up)<BR>\n" );
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document.write( "(d) If this is not a reasonable requirement, suggest one that is.<BR>\n" );
document.write( "Increase E or decrease the confidence level; both will have the<BR>\n" );
document.write( "effect of lowering \"n\".<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );