Chapter 11.2, Problem 12PB

First and second free throw independent? In pro basketball games during 1980–1982, when Larry Bird of the Boston Celtics made his first free throw, 251 out of 285 times he made the second one, and when he missed his first free throw, 48 out of 53 times he made the second one.

1. a. Form a 2 × 2 contingency table that cross-tabulates the outcome of the first free throw (with categories made and missed) and the outcome of the second free throw (made and missed).
2. b. When we use MINITAB to analyze the contingency table, we get the result

Pearson Chi-Square = 0.273, DF = 1, P-Value = 0.602

Does it seem as if his success on the second shot depends on whether he made the first? Explain how to interpret the result of the chi-squared test. (Here, for the chi-squared test to apply, we assume that each pair of free throws attempted is independent of any other pair during the same or other games. This is reasonable in professional sports.)