Castaneda v. Partidais 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 phrase "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 thezstatistic and correspond toP-values of approximately 0.05 and 0.0026.) InCastanedathe 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 were181,100persons eligible for jury duty, of whom142,725were Mexican Americans. Of the885people selected for jury duty,348were Mexican Americans.

(a) What proportion of eligible voters were Mexican Americans? Let this value bep_o. (Round your answer to four decimal places.)

(b) Letpbe the probability that a randomly selected juror is a Mexican American. The null hypothesis to be tested isH_o:p=p_o. Find the value ofpfor this problem, compute thezstatistic, and find theP-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 facie case. The burden of proof then shifts to the defense.) (Use= 0.01. Round your test statistic to two decimal places and yourP-value to four decimal places.) z= p-value=

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(c) We can reformulate this exercise 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 Americans among those not selected as jurors. Letp₁be the probability that a randomly selected juror is a Mexican American, and letp₂be the probability that a randomly selected nonjuror is a Mexican American. Find thezstatistic and itsP-value. (Use= 0.01. Round your test statistic to two decimal places and yourP-value to four decimal places.) z= p-value=

Conclusion??

How do these answers compare with your results in (b)?