47. A problem of interest in baseball is whether a sacrifice bunt is a good strategy when there is a man on first base and no outs. Assuming that the bunter will be out but will be successful in advancing the man on base, we could compare the probability of scoring a run with a player on first base and no outs with the probability of scoring a run with a player on second base and one out. The following data resulted from a study of randomly chosen major league baseball games played in 1959 and 1960.

(a) Give a 95 percent confidence interval estimate for the probability of scoring at least one run when there is a man on first and no outs.

(b) Give a 95 percent confidence interval estimate for the probability of scoring at least one run when there is a man on second and one out.

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Number Base Occupied of Outs First Second 0 Number of Cases in Which 0 Runs Are Scored 1,044 Total Number of Cases 1,728 1 401 657