Question: In professional basketball games, the fans of the home team always try to distract free throw shooters on the visiting team. To investigate whether this tactic is actually effective, the free throw statistics of a professional basketball player with a high free throw percentage were examined. During the entire last season, this player had 656 free throws, 420 in home games and 236 in away games. The results are summarized below.
a. Give a point estimate for the difference in the proportion of free throws made at home and away.
b. Construct the 90% confidence interval for the difference, based on these data.
c. Test, at the 10% level of significance, the hypothesis that there exists a home advantage in free throws.
d. Compute the p-value of the test.