Question

Census data for a certain county show that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty and only 9 of them are Hispanic. Does this apparent under-representation of Hispanics call in to question the fairness of the jury selection system? Explain.

Note that for this stated problem, we have X=9, n=72, p-hat=9/72=12.5%, and p=19%. Since we are in the Binomial Setting, we have X~B(72, 0.19), and E(X)=13.68 is the expected value of X. Note this means that our actual observation of X=9, fell 4.68 units away from the expected value E(X)=13.68 here.

a) Using the given Binomial model: Find the probability of falling at least as far away from expected as we actually observed, meaning 4.68 or more away from 13.68 (in either direction). Note that the probability we find here, is called the P-value, and the process we are performing here is called a two-sided significance test.

b) Considering the probability that you found in part (a) above: Do you feel that the lower number of Hispanics in our sample is best explained by random chance, or do you instead feel that it indicates something is broken in our model? Explain your reasoning for your choice.

Answer 1