Castaneds v. Partida is an important court case in which statistical methods wer

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Castaneds v. Partida is an important court case in which statistical methods were used as part of a legal argument. When reviewing this case, the Supreme Court used the phrasc "two or three standard deviations as a criterion for statistical significance This Supreme Court review has served as the basis for many subsequent applications of statistical methods in legal settings. (The two or three standard deviations referred to by the Court are values of the z statistic and correspond to P-values of approximately 0.05 and 0.0026.) In Castaneds 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 180,350 persons eligible for jury duty, of whom 143,225 were Mexican Americans. Of the 868 people selected for jury duty, 336 were Mevican Americans a) what proportion of eligible voters were Mexican Americans? Let this value be pa (Round your answer to four decimal places.) b) Let p be the probability that a randomly selected juror is a Mexican American. The null hypothesis to be tested is H p -pa Find the value ofs for this problem, compute the z statistic, and find the P-value, What do you conclude? (A finding of statistical significance in this circumstance does not constitute a proof of discrimination. It can be used however to establish a prima acle case The burden of proof then shifts to the detense use ? ?.01. Round your test statistic to two decimal places and your P-value to four decimal places.) P-valua O Rgjact tha null hypothasis, thara is significant avidance that Maxican Americans are undarraprazentad on jurias. O Reject the null hypothesis, there is not significant evidence that Mexican Americans are underrepresented on juries. O Fail to reject the null hypothesis, there is not signifcant evidence that Mexican Americans are underrepresented on juries. O Fail to reject the null hypothasis, there is significant avidence that Maxican Americans are underraprazented on juries. c) we can reformulate this exercise as a two-sample problem. Here ve wish to compare the proportion of Mexican Americans among ose selected as urors with the proportion of Mexican Americans among those not selected as urors. Let ?,be the probability 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. Use ?-0.01. Round your test statistic to two decima placas and your P-valua to four dacimal placas.) P-valua Rejact the null hypothasis, thera is significant avidance of a difference in proportions. O Reject the null hypothesis, there is not significant evidence of a difference in proportions. O Fail to reject the null hypothesis, there is not significant evidence of a difference in proportions. Fail to rejact tha null hypothasis, thara is significant avidanca of a diffaranca in proportions. How do your answers compare with your results in (b)? vary diffarant very similar O none of the above

Explanation / Answer

(a)

Here p0 = 143225/180350 = 0.7942

(b) Here population proportion p^ = 336/868 = 0.3871

Here

standard error of proportion = sqrt [0.7942 * (1 - 0.7942)/868] = 0.0137

Z = (0.7942 - 0.3871)/0.0137 = 29.66

P - value = 0.0000

Here reject the null hypothesis, there is significant evidence that mexican Americans are underrepresented on juries.

(c) Here standard error of difference in proportion = sqrt [0.7942 * (1 - 0.7942)/180350 + 0.3871 * (1 - 0.3871)/868] = 0.0166

Z = (0.7942 - 0.3871)/0.0166 = 24.58

P - value = 0.0000

Reject the null hypothesis, there is significant evidence that mexican Americans are underrepresented on juries.

Here the results are very similar.

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