# Confidence Interval for the True Mean

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

8.65 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].)

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#### Solution Summary

The solution examines the confidence interval for the true mean.