Discussion:
Q1: 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
Q2: A careful count of 13,789 carcasses of bugs killed by "mosquito zappers" used in homes near water showed that only 18 were mosquitoes. (a) Construct a 90 percent confidence interval for the proportion of all zapped bugs that are mosquitoes. (b) Is a confidence interval really helpful in deciding whether the devices fulfill their purpose? Explain. (Data are from Scientific American 276, no. 4 [June 1997].)