7.9 Baseballs vary somewhat in their rebounding coefficient. A baseball that has a large rebound coefficient will travel farther when the same force is applied to it than a ball with a smaller coefficient. To achieve a game in which each batter has an equal opportunity to hit a home run, the balls should have nearly the same rebound coefficient. A standard test has been developed to measure the rebound coefficient of baseballs. A purchaser of large quantities of baseballs requires that the mean coefficient value be 85 units and the standard deviation be less than 2 units. A random sample of 40 baseballs is selected from a large batch of balls and tested. The data are given here. 84.8 88.1 85.1 88.0 86.6 85.3 85.1 91.4 83.4 87.2 83.7 89.5 85.6 83.5 81.6 81.1 83.6 81.2 84.7 87.0 87.5 84.3 86.9 83.3 85.9 82.2 88.2 83.5 82.7 86.0 87.3 87.9 82.6 80.5 85.6 82.3 79.3 84.9 80.6 83.9 a. Do the data indicate any violations in the conditions necessary to use the chi-square procedures for generating confidence intervals and testing hypotheses? b. Estimate the standard deviation in the rebound coefficients using a 99% confidence interval. c. Do the data indicate that the mean rebound coefficient is less than 85? Use a 5 .05 in reaching your conclusion. d. Do the data indicate that the standard deviation in rebound coefficients exceeds 2? Use a 5 .01 in reaching your conclusion. e. To what population can the inferences obtained in parts (b)–(d) be validly applied?
7.9
Baseballs vary somewhat in their rebounding coefficient. A baseball that has a large rebound coefficient will travel farther when the same force is applied to it than a ball with a smaller coefficient. To achieve a game in which each batter has an equal opportunity to hit a home run, the balls should have nearly the same rebound coefficient. A standard test has been developed to measure the rebound coefficient of baseballs. A purchaser of large quantities of baseballs requires that the mean coefficient value be 85 units and the standard deviation be less than 2 units. A random sample of 40 baseballs is selected from a large batch of balls and tested. The data are given here.
| 84.8 | 88.1 | 85.1 | 88.0 | 86.6 | 85.3 | 85.1 | 91.4 | 83.4 | 87.2 |
| 83.7 | 89.5 | 85.6 | 83.5 | 81.6 | 81.1 | 83.6 | 81.2 | 84.7 | 87.0 |
| 87.5 | 84.3 | 86.9 | 83.3 | 85.9 | 82.2 | 88.2 | 83.5 | 82.7 | 86.0 |
| 87.3 | 87.9 | 82.6 | 80.5 | 85.6 | 82.3 | 79.3 | 84.9 | 80.6 | 83.9 |
a. Do the data indicate any violations in the conditions necessary to use the chi-square procedures for generating confidence intervals and testing hypotheses?
b. Estimate the standard deviation in the rebound coefficients using a 99% confidence interval.
c. Do the data indicate that the mean rebound coefficient is less than 85? Use a 5 .05 in reaching your conclusion.
d. Do the data indicate that the standard deviation in rebound coefficients exceeds 2? Use a 5 .01 in reaching your conclusion.
e. To what population can the inferences obtained in parts (b)–(d) be validly applied?
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