Racial bias in jury selection is a complex situation this pr

Racial bias in jury selection is a complex situation; this project oversimplifies the issue so we can explore it with the statistical tools in this chapter. However, it is important to remember that statistics is only one tool among many. Several types of information are needed to determine the truth behind the issue of racial discrimination.

Suppose that 12 people are chosen at random for a jury from a large population in which 40% are black and 60% white.

6. Argue that the number of black persons chosen for the jury has (at least approximately) the binomial distribution with parameters n = 12 and p = 0.4.

Hence, the probability that there are x black persons on the jury is

f(x) = C(12, x) 0.4^x 0.6^{12 - x} for x = 0, 1, ..., 12,

where C(12, x) is the binomial coefficient 12! / [x! (12 - x)!].

7. Explicitly compute the probabilities in the previous exercise to verify the following table:

8. Criticize the binomial model for the process of jury selection. Which of the three assumptions in the binomial model may be violated?

9. Sketch the histogram of the probability distribution in Exercises 6 and 7

10. Calculate the mean and standard deviation of the Number Selected variable.

11. In Horsley\'s trial, there were no blacks on the jury. Assuming the binomial model above, what is the probability of this event. Do you think that such a probability value indicates racial bias?

Solution

The criticism for Binomial process applied here are:

1) There may be race discrimination. So we cannot assume prob of selecting black is exactly 0.4

2) Each trial may not be independent of the other.

The others are adhered to such as 2 bernoulli outcomes etc.

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Mean = np = 12(0.4) = 4.8

Variance = npq = 0.288

std dev = 0.537

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Prob for no black jury = bin prob (x=0) = (0.6)¹²