Over the past three complete Major League Baseball seasons, 2015-2017, the average length of a game was 172 minutes; forty-five percent of games lasted longer than three hours. Final figures for the 2018 season are not yet available but in a random sample of 102 games from the 2018 seasons the following figures were obtained

Average length 177.1 minutes

SD of length 19.2 minutes

Number games > 3 hours 49

(a) Compute a 90% confidence interval for the season-long mean game length ().

(b) Use your interval in part (a) to test whether the mean game length for 2018 has changed significantly from the average for the past three seasons. Be sure to state your hypotheses, carefully state your conclusion. What level of significance is implicit in your conclusion?

(c) Compute a 95% confidence interval for the proportion (p) of all games in 2018 that lasted longer than three hours.

(d) Use you interval in part (c) to test whether the fraction of games lasting more than three hours in 2018 differs significantly from the figure over the past three seasons. Be sure to state your hypotheses, carefully state your conclusion. What level of significance is implicit in your conclusion?