This problem concerns the duration of US major league baseball games. In the early 2000s, Major League Baseball was concerned about the declining television ratings of baseball. One factor considered was the length of games—did they last too long?

For fans of other sports, here is some background relevant to this problem. Baseball has no time limit—the two teams alternate at-bats for a total of nine innings (each team’s at-bat is a half-inning). If the two teams are tied at the end of nine innings, the two teams continue playing until one team is ahead at the end of a full inning. In the National League, pitchers (who are poor hitters) are required to bat. In the American League, the pitcher is not required to hit, and the pitcher’s position in the batting order is taken by a designated hitter.

Here are the durations (hours:minutes) of games played on September 13, 2011:

2:29 (N)

2:33 (N)

2:53 (N)

3:02 (A)

2:56 (N)

3:23 (A)

3:07 (A)

3:50 (N) (11 innings)

2:20 (A)

2:41 (A)

3:08 (N)

(a) Based on this sample, derive a point estimate for the AVERAGE duration of baseball games.

(b) Derive a confidence interval around that point estimate; you can use either resampling (bootstrap) or formula (by hand or software).

(c) Calculate two separate point estimates, one for National League games and the other for American League games.

(d) Comment on the difference between the two and the possible reason(s).

(e) What is the population that you are making an inference to, in part b? Is it reasonable to assume that it is Normally shaped?

(f) Is this a random sample? Comment on the validity of the sampling method.