1. Suppose that the manager of the Cleveland Indians is faced with a difficult situation in the last inning of a baseball game later this evening and he asks for your input. Here is the situation. He has two right-handed batters, say Moe and Joe, available to pinch hit in the last inning to try to win the game. However, he is not sure which player to use. The performance of the players during the 1995 season is shown in the table below.
 
Player Pitcher Hits At Bats
Joe Right 40 100
Left 80 400
Moe Right 120 400
Left 10 100

a. Construct a two-way table of player (Joe or Moe) versus outcome (hit or no hit).

b. Compute the overall batting average (hits divided by total number of times at bat) for each of the players.

c. For each of the two types of pitching, construct a two-way table of player by outcome (hit or no hit).

d. Use the tables in part (c) to compute the batting averages of the two players for each type of pitcher.

e. Based on the calculations in (b) and (d), who would you recommend? Explain your recommendation in language that the manager will understand.

2.  The University of California at Berkeley was charged with having discriminated against women in the graduate admissions process for the fall quarter of 1973. The table below identifies the number of acceptances and denials for both male and female applicants in each of the six largest graduate programs at the institution at that time:
 
 
Men Accepted Men Denied Women Accepted Women Denied
Program A 511 314
Program B 352 208
Program C 120 205
Program D 137 270
Program E 53 138
Program F 22 351
Total 1195 1486 559 1276

Men accepted Men denied Women accepted Women denied
Program A 511 314 89 19
Program B 352 208 17 8
Program C 120 205 202 391
Program D 137 270 132 243
Program E 53 138 95 298
Program F 22 351 24 317
Total 1195 1486 559 1276

(a) Start by ignoring the program distinction, collapsing the data into a two-way table of gender by admission status. To do this, find the total number of men accepted and denied and the total number of women accepted and denied.

Admitted Denied Total
Men
Women
Total

(b) Consider for the moment just the men applicants. Of the men who applied to one of these programs, what proportion were admitted? Now consider the women applicants; what proportion of them were admitted? Do these proportions seem to support the claim that men were given preferential treatment in admissions decisions?

(c) To try to isolate the program or programs responsible for the mistreatment of women applicants, calculate the proportion of men and the proportion of women within each program who were admitted. Record your results in a table like the one below.

                    Proportion of men admitted Proportion of women admitted
Program A
Program B
Program C
Program D
Program E
Program F
 

(d) Does it seem as if any program is responsible for the large discrepancy between men and women in the overall proportions admitted?