2. You are to investigate whether there exists a pattern of racial discriminatio

Question

2. You are to investigate whether there exists a pattern of racial discrimination in the selection of Federal juries in a southwestern state. You have only the following data and your understanding of statistics to determine whether the selection of juries follows a random or nonrandom pattern. In this Federal Court District, 35 percent of the adult population who may serve on juries are Latino while the other 65 percent are white. In this Federal Court a pool of 20 adults are randomly selected from the general population for each jury trial. These jury pools are randomly drawn from the voter regltration lists. From this group of 20, the trial attorneys representing both sides, mutually select a jury of six plus two alternates making eight. Data has been collected on the racial composition for all of the jury pools and the actual juries (of eight) selected in this District for the past ten years. Of all of jury pools , about 1.15% have had no Latinos on the jury pool, over 60 % of the pools have had four or fewer on the jury pool, and less than 1 % of the jury pools have had a majority of Latinos on the jury pool. Lastly, the average number of Latinos on these jury pools has been 4.0. Of all of the lures, about 16.78 % have had no Latinos, only a little better than 1% have had a majority of Latinos, and the average number of Latinos has averaged 1.6 per jury

Explanation / Answer

Let X be a random variable which denotes the number of Lations in the jury pools

(a) For given Binomial Distribution we use the general population figures n=20 and p=0.35

The pmf of a binomial distribution is given by: P(X=x) = nCxpx(1-p)n-x

So, we have the following probability table:

P(X=0) = 0.000181

P(X4) = P(X=0) +P(X=1) + P(X=2) + P(X=3) + P(X=4) = 0.000181 + 0.001925 + 0.009985 +0.032258 + 0.073821 = 0.118197

Similarly, P(X>10) = 1- p(X<=10) = 1- 0.946833 =0.053167

X4

The mean is given by E(X) = np = 20x0.35 = 7.

From the data given we have the following values:

On comparing the two information we conclude that there is certain level of discrimination against latinos in the selection of jury.

(b) For the new information given we have in a jury of 20 there are 4 latios and 20 whites.

So, for the new binomial distribution we have n=20 and p=4/20 = 0.2

So, we have the following probability table:

P(X=0) = 0.011529

P(X>=4) = 1-P(X4) = 1- {P(X=0) +P(X=1) + P(X=2) + P(X=3)} = 1-{0.011529 +0.057846 + 0.136909 + 0.205364} = 1-0.411449 = 0.588551

The Expected value of the Latinos in the jury are E(X) = np = 20x0.2 = 4.

On comparing with the given data we can conclude that there might be a MORE probability of having 4 or more latinos in the jury using the given binomial distribution.

(c) If no discrimination existed then we might have the probability of selecting a latino equal to the probability of selecting a white. So, for this binomial distribution we have n=20 and p=0.5

So, we have the following probability table:

The Expected value of the Latinos in the jury are E(X) = np = 20x0.5 = 10.

This data suggests that discrimination does infact exists in the jury system.

Event Probability X=0 0.000181

X4

0.118197 X>10 0.053167

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