# Sample Essay

266 WordsNov 20, 20112 Pages
8.48 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: 0 260 356 403 536 0 268 369 428 536 268 396 469 536 162 338 403 536 536 130 (a) Construct a 95 percent confidence interval for the true 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 are from a project by MBA student Daniel R. Dalach.) DisplayAds A: n=20, Mean x=346.5, standard deviation s=170.38 Since n&lt;30, we must use t-table: d.f =19 For 95% confidence α=0.05, a/2=0.025 From t-table at d.f=19=2.093 Confidence interval=346.5 2.903×(170.38/20)=346.5 79.74= (266.76, 426.24) Confidence interval is (266.76, 426.24) B: Normality may be an issue because the sample of 20 may not have been selected from the population in a random manner. C: Standard deviation=170.38 E=10=99%, Z=2.576 Sample size n=ZE2 D: 99% confidence may be too high for a distribution that may not be normal. Dropping the confidence may reduce the required sample