Question 9.34

9.34 Discrimination?

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

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Business
Admit Deny
Male 480 120
Female 180 20
Law
Admit Deny
Male 10 90
Female 100 200

Note that you answered parts (a) through (d) of this exercise if you completed Exercise 2.116 (page 116).

  1. Make a two-way table of gender 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.

    479

  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.
  5. Use the data summary that you prepared in part (a) to test the null hypothesis that there is no relationship between gender and whether or not an applicant is admitted to a professional school at Wabash Tech.
  6. Test the same null hypothesis using the business school data only.
  7. Do the same for the law school data.
  8. Compare the results for the two schools.