Question

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Question 3 (20 pts In a court case reviewed by the Supreme Court the plaintiffs alleged that the method for selecting juries in a county in Texas was biased against Mexican Americans. For the period of time at issue, there were 181,535 persons eligible for jury duty, of whom 143, 611 were Mexican Americans. Of the 870 people selected for jury duty, 339 were Mexican Americans. a. What proportion of eligible jurors were Mexican Americans? Denote this value by po. b. Let p be the probability that a randomly selected juror is a Mexican American. The null hypothesis to be tested is Ho:p=Po Find the value of p for this problem, compute the 2-statistic, and estimate the p-value. What do you conclude? c. Reformulate the problem as a two-sample problem. Here we wish to compare the proportion of Mexican Americans among those selected as jurors with the proportion of Mexican Ameri- cans among those not selected as jurors. Let pl be the probabil- ity that a randomly selected juror is a Mexican American, and let P2 be the probability that a randomly selected nonjuror is a Mexican American. Find the z-statistic and its p-value. How do your answers compre with your results in part (b)?

Answer 1

p-value= axP(2 4 2 - 0 2xP (2= -29.13) = [0.0000] Since p-value La=0.os ( significance level), we reject Ho. hond he conclude that there is enough evidence to suggest that the method for selecting joves is kiased against Mexican Americans. (es To test, Ho : p. = p2 us. Hi bizko (null) Now, bê= sample proportion or jurars who are Mexican American. = 339 03497 h = sample proportion or non jurors who are Mexican n o American = 143611 - 339 13272 181535-470180665 = 0.7930 Now, ô = pooled proportion = 339 + 143272 14364 870 + 180 365 181535 = 0.7911 Also, ni = 87o, n2 = 180665 vatistica 2 Statistica Zo= red .: Test pi b ê . VA (ITP) (1 2 + 1 h) 1 29,20) 'p-value - 0 2x P(25-29,20) = 0.00007 Since p-value La= 0.05, we reject to. The crswers in part (b) and part of some se be o both the coses it showing then the method it cs Shiored wit against Mexican Americans Cascame - are same because