12.4 The article “In Bronx, Hitting Home Runs Is A Breeze”

(USA Today, June 2, 2009) included a classification of 87 home runs hit at the new Yankee Stadium according to the direction that the ball was hit, resulting in the accompanying data.

Direction Left Field Left Center Center Right Center Right Field Number of Home Runs 18 10 7 18 34

a. Assuming that it is reasonable to regard this sample of 87 home runs as representative of home runs hit at Yankee Stadium, carry out a hypothesis test to determine if there is convincing evidence that the proportion of home runs hit is not the same for all five directions. (Hint: See Example 12.2.)

b. Write a few sentences describing how the observed counts for the five directions differ from what would have been expected if the proportion of home runs is the same for all five directions.