Refer to Table 3.7, which classifies police officers by rank, race, and promotion decisions made in 1988.

a. Conduct an exact test of conditional independence of promotion and race, given rank. Interpret, and compare results to the large-sample test.

b. Conduct an exact test of whether the odds ratio is identical for the four ranks. Interpret, and compare results to the large-sample test.

c. Construct and interpret a confidence interval for an assumed common odds ratio.

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Table 3.7 Sergeant Promotions SA Sergeant Promotions Master Sgt SA Master Sgt Promotions Promotions Race Yes No Yes No Yes No Yes No Black 4 103 1 35 2 18 1 4 White 43 548 4 109 43 155 18 94 Source: Dixon vs. Margolis, 56 FEP Cases 401 (N.D. Illinois, 1991), as quoted by J. Gastwirth and C. Mehta in The usefulness of exact statistical methods in equal employment litigation, in Computational Statistics, Vol. 2, Y. Dodge and J. Whittaker, eds. (Berlin: Springer-Verlag, 1992), pp. 91-95.