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

Question

Castaneda 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 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 or 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 Castaneda 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, 900 persons eligible for Jury duty, of whom 143, 525 were Mexican Americans. Of the 867 people selected for jury duty, 340 were Mexican Americans. (a) what proportion of eligible voters were Mexican Americans? Let this value be p_e. (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_o: p = p_o. Find the value of p 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 facie case. The burden of proof then shifts to the defense.) (Use alpha = 0.01. Round your test statistic to two decimal places and your P-value to four decimal places.)

Explanation / Answer

a) Po = 142675/180525 = 0.7903

b) Ho: p = 0.7903
Ha: p < 0.7903, if there is evidence to suggest that Mexican Americans are under-represented in Juries

Of the 867 people, 340 were Mexican Americans, p = 340/867 = 0.3922

z = (p-p0)/sqrt(p0(1-p0)/n) = (0.3922-0.7903)/sqrt(0.7903(0.2097)/867) = -28.79
p = 0
Reject the null hypothesis, there is significant evidence that mexican americans are underrepresented on juries

c)
p1 = proportion of selected jurors that are mexican americans = 340/143525
p2 = proportion of selected jurors that are not mexican americans = (867-340)/(180900-143525)=527/37375

H0: p2 - p1 = 0
Ha: p2 - p1 > 0

pooled estimate, p_hat = (p1n1+p2n2)/(n1+n2) = ((340/143525)*143525 + (527/37375)*37375)/(143525+37375)
p_hat = 0.004792703151

Standard Error, SE = sqrt(p_hat(1-P_hat)((1/n1)+(1/n2))) = sqrt(0.0047927(0.9952073)((1/143525)+(1/37375)))
SE = 0.0004010624

z = (p2-p1)/SE = ((527/37375)-(340/143525))/0.0004010624 = 29.25
P-value = 0, P-value < 0.01

Reject the null hypothesis, there is significant evidence of difference in proportions.

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