Question: A minor league baseball executive has become concerned about the slow pace of games played in her league, fearing that it will lower attendance. She meets with the league's managers and umpires and discusses guidelines for speeding up the games. Before the meeting, the mean duration of nine-inning games was 3 hours, 5 minutes (i.e., 185 minutes). A random sample of 36 nine-inning games after the meeting showed a mean of 179 minutes with a standard deviation of 12 minutes.

a. Testing at the 1% significance level, can you conclude that the mean duration of nine-inning games has decreased after the meeting?

b. What is the Type I error in part a? What is the probability of making this error?

c. What will your decision be in part a if the probability of making a Type I error is zero? Explain.

d. Find the range for the p-value for the test of part a. What is your decision based on this p-value?