Racial bias in jury selection is a complex situation; this project oversimplifie

Question

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.

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?

Explanation / Answer

Question 9 and 10 require information about the previous question. So I am giving answers of 8,10

8) here the given information satisfies the conditions of binomial distribution. That is

Define X be the random variable denoting number of black in sample.

First X can be classified into two different types that is success and failure. Getting black is success and getting white is failure. That is there is two possible outcomes also they are mutually exclusive.

Secondly the trial of drawing samples are independent. As first draw we get suppose black in next draw it completely independent of the first draw to get black or white.

Thirdly here sample size 12 is fixed previously. In any circumstances that sample size will not changed.

10) here X is binomial random variable with parameters n=12, and p=0.4

So mean = E(X) =12*0.4=4.8

Variance = E(X) = 12*0.4*(1-.4)=2.88

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