12.4 The article “In Bronx, Hitting Home Runs Is A Breeze” (USA Today, June 2, 2009) included a classifi- cation of 87 home runs hit at the new Yankee Stadium according to direction that the ball was hit, resulting in the  accompanying data.

 

Number of Correct Identifications 0 1 2 Observed Count 21 10 13

describes an interesting experiment to determine if college students can identify their roommates by smell. Forty-four female college students participated as subjects in the ex- periment. Each subject was presented with a set of three t-shirts that were identical in appearance. Each of the three t-shirts had been slept in for at least 7 hours by a person who had not used any scented products (like scented de- odorant, soap, or shampoo) for at least 48 hours prior to sleeping in the shirt. One of the three shirts had been worn by the subject’s roommate. The subject was asked to iden- tify the shirt worn by her roommate. This process was then repeated with another three shirts, and the number of times out of the two trials that the subject correctly identified the shirt worn by her roommate was recorded. The resulting data is given in the accompanying table.

 

	Direction Left     Left Field   Center Center   Right        Right Center   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.

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.