For Exercise 2.91, see page 106; for 2.92 and 2.93, see pages 106–107; for 2.94 to 2.96, see page 108; for 2.97 to 2.99, see page 109; and for 2.100 and 2.101, see pages 111–112.

Question 2.116

2.116 Discrimination?

Wabash Tech has two professional schools, business and law. Here are two-way tables of applicants to both schools, categorized by sex and admission decision. (Although these data are made up, similar situations occur in reality.)

disc

Business
Admit Deny
Male 480 120
Female 180 20
Law
Admit Deny
Male 10 90
Female 100 200
  1. Make a two-way table of sex by admission decision for the two professional schools together by summing entries in these tables.
  2. From the two-way table, calculate the percent of male applicants who are admitted and the percent of female applicants who are admitted. Wabash admits a higher percent of male applicants.
  3. Now compute separately the percents of male and female applicants admitted by the business school and by the law school. Each school admits a higher percent of female applicants.
  4. This is Simpson's paradox: both schools admit a higher percent of the women who apply, but overall, Wabash admits a lower percent of female applicants than of male applicants. Explain carefully, as if speaking to a skeptical reporter, how it can happen that Wabash appears to favor males when each school individually favors females.