Chapter 8.2, Problem 22P

Baseball: Home Run Percentage The home run percentage is the number of home runs per 100 times at bat. A random sample of 143 professional baseball players gave the following data for home run percentages (Reference: The Baseball Encyclopedia, Macmillan).

1.6	2.4	1.2	6.6	2.3	0.0	1.8	2.5	6.5	1.8
2.7	2.0	1.9	1.3	2.7	1.7	1.3	2.1	2.8	1.4
3.8	2.1	3.4	1.3	1.5	2.9	2.6	0.0	4.1	2.9
1.9	2.4	0.0	1.8	3.1	3.8	3.2	1.6	4.2	0.0
1.2	1.8	2.4

(a) Use a calculator with mean and standard deviation keys to verify that $\bar{x}\approx 2.29\text{and}s\approx \mathrm{1.40.}$

(b) Compute a 90% confidence interval for the population mean µ of home run percentage for all professional baseball players. Hint: If you use Table 4 of the Appendix, be sure to use tile closest d.f. that is smaller.

(c) Compute a 99% confidence interval for the population mean µ of home run percentages for all professional baseball players.

(d) Interpretation The home run percentages for three professional players are

Tim Huelett, 2.5 Herb Hunter, 2.0 Jackie Jensen, 3.8

Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.

(e) Check Requirements In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: See the central limit

theorem in Section 7.5.