Simulating Probabilities

 Practice Problems

From Activity Based Statistics...

1) In 1972, 48 male bank supervisors were given the same personnel files and asked to judge whether the person should be promoted to a branch manager job that was described as "routine" or the person's file held and other applicants interviewed. The files were identical, except that half of them showed that the person was female and half shows that the file was that of a male. Of the 24 "male" files, 21 were recommended for promotion. Of the 24 "female" files, 14 were recommended for promotion.

Is this convincing evidence that the bank supervisors discriminated against female applicants? Could the difference in the numbers recommended for promotion reasonably be attributed to chance?

(B. Rosen and T. Jerdee(1974), "Influence of sex role stereotypes on personnel decisions," Journal of Applied Psychology, 59:9-14.)

NOTE: You can simulate this using cards. When you've finished, read this, which shows how you might use this simulation in the classroom. (From Franklin, Christine and Gould, Robert, "Teaching Statistics to High School Teachers", Proceedings of the MET Summit Conference, November 2001.)

2) Few situations in real life are as clear cut as that of the bank managers. In real life the files are never identical. Education, experience, character, recommendations, and test scores vary. Statistics can tell us only whether the differences between groups can reasonably be attributed to chance. In Griggs v. Duke Power Company (1971) the Supreme Court established the idea of a "disparate impact." Disparate impact occurs when the pass rate of one group on an employment test is substantially lower than that of another. Such an  employment test is illegal unless an employer can prove that the use of the test is a business necessity. Simulate one of the following situations below and write your conclusions clearly and completely.

a) In the 1975 court case Chicano Police Officers Association v. Stover, three of the 26 Chicanos passed an exam and 14 of the 64 whites passed the same examination.

b) In the 1977 Dendy v. Washington Hospital case, 26 of 26 white nurses passed an exam and 4 of 9 African-American nurses passed the same exam.