Racial Bias in Jury Selection
(Extra Credit Assignment)

Directions: Don’t hand in this sheet but work each problem on separate paper. Work carefully because you need to get each question right to answer the later questions correctly. Show any calculations, as usual. Give all answers to four decimal places.

Each question counts ½ extra-credit point, for a total of 3½. (This goes in one of the “other” blocks in the extra-credit section of your grade calculator.)

The Data

This is a true story. A black man was convicted of raping a white woman and was sentenced to death. His attorney argued in the appeal that the jury had no blacks and was therefore racially biased since the county was 26% black. The appeal failed because the court ruled the jury selection wasn’t racially biased.

Jury selection proceeded as follows: At the time, only men over 21 were eligible. A panel of 100 men over 21 was selected, supposedly randomly, and the panel contained eight blacks. The actual jury was selected from among the 100 men on the panel.

The Problems

1. Each member of the panel of 100 was either black or not black, and (assuming random selection) the choices were all independent. What kind of probability distribution does that represent?
2. Using the techniques you know for that type of distribution, find the probability that 100 randomly selected men would contain 8 blacks or fewer, if the population is 26% black.

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   Now use the Central Limit Theorem to rework the problem in the following steps. (The 26% or 0.26 figure is actually a proportion not a mean, but you treat it like a population mean to do the calculations.)

3. The population standard deviation is 0.438634. Compute the standard error for sample size 100. (Use symbol σ_p̂ rather than σ_x̄ — we’ll see why in week 11.)
4. The actual proportion of blacks on the panel was 8% or 0.08. Use that, the population figure of 0.26, and your standard error to compute the z-score.
5. Sketch the normal curve for the sampling distribution of this sample size. Shade the area representing less than 0.08 in the sample. Instead of x̄ and z axes you’ll have p̂ and z axes — again, we’ll learn why in week 11.
6. Use the z-score to find the probability of finding a sample with 0.08, which is the shaded area. This is the probability of finding a truly random sample of 100 men with 8% blacks or fewer, in a population that is 26% black. (This won’t exactly equal your answer to problem 2.)
7. Based on the probability, do you believe the actual composition of the panel of 100 could have been the result of random selection, or does it appear that it was racially biased? Answer in a short sentence explaining your reasoning.