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.
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 α = .05 in reaching your conclusion.
d. Do the data indicate that the standard deviation in rebound coefficients exceeds 2? Use α = .01 in reaching your conclusion.
e. To what population can the inferences obtained in parts (b)–(d) be validly applied?

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