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# Statistics: Hypothesis, Probability, Decision Rule

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All text problem assignments must include the problem statement, calculations, formulas, and your method of analysis. Problems should be done in excel - copied and paste into word doc.

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.)

The mean annual turnover rate of the 200-count Bayer Aspirin is 6.0 with a standard deviation of 0.50. (this indicates that the stock of Bayer turns over on the pharmacy shelves an average of 6 times per year.) It is suspected that the mean turnover has changed and is not 6.0. Use the .05 significance level.
a. state the null hypothesis and the alternate hypothesis
b. what is the probability of the Type I error?
c. give the formula for the test statistic
d. state the decision rule
e. a random sample of 64 bottles of the 200-count size Bayer Aspirin showed a mean turnover rate of 5.84. Shall we reject the hypothesis that the population mean is 6.0? Interpret the result.