In Major League Baseball, the umpire behind the plate uses his best judgment to decide if a pitch is within the strike zone or outside of the strike zone. The age-old question is whether the strike zone for the batter in the National League is different from the strike zone in the American League. One way to address this question is to compare the percentage of called third strikes in the two leagues.

The logic is that a batter who looks at a called third strike without swinging believed the pitch was outside the strike zone when the umpire considered the pitch within the strike zone. To test this hypothesis, a random sample of plate appearances from each league was selected and the number of called third strikes was counted. The data are as follows:

American National x1 = 46 x2 = 37 n1 = 170 n2 = 160

a. Perform a hypothesis test with a = 0.10 to determine if the proportion of called third strikes differs between the two leagues.

b. Determine the p-value and interpret the results.

c. Construct a 90% confidence interval to estimate the difference in the proportion of called third strikes between the two leagues.

d. Verify your results using PHStat.

AppendixLO1