Castaneda v. Partida is an important court case in which statistical methods wer
ID: 3311258 • Letter: C
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 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 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 181,875 persons eligible for jury duty, of whom 143,875 were Mexican Americans. Of the 853 people selected for jury duty, 335 were Mexican Americans.
(a) What proportion of eligible voters were Mexican Americans? Let this value be po. (Round your answer to four decimal places.)
1
(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 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 = 0.01. Round your test statistic to two decimal places and your P-value to four decimal places.)
Conclusion: Pick 1
Reject the null hypothesis, there is significant evidence that Mexican Americans are underrepresented on juries.
Reject the null hypothesis, there is not significant evidence that Mexican Americans are underrepresented on juries.
Fail to reject the null hypothesis, there is not significant evidence that Mexican Americans are underrepresented on juries.
Fail to reject the null hypothesis, there is significant evidence that Mexican Americans are underrepresented on juries.
(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. Let p1 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 decimal places and your P-value to four decimal places.)
Explanation / Answer
Solution:
a) The proportion of eligible voters who were Mexican Americans is obtained as shown below:
From the information given, out of 181,875 persons eligible for jury, 143,875 were Mexican Americans.
p0 = X/N = 143,875/181,875
= 0.7911
The proportion of eligible voters who were Mexican Americans is 0.7911
b) From information given, out of 853 selected for jury, 335 were Mexican Americans. The sample proportion is,
p = x/n = 335/853 = 0.3927
The sample proportion is obtained by taking the ratio of number of success (x) and the sample size n.
The value os z-statistic is obtained as shown below:
z = p - p0 /sqrt[p0(1-p0)/n]
= (0.3927 - 0.7911)/sqrt[0.7911(1-0.7911)/853]
= -28.62
p-value = 0.0001
c)
The value of z statistic is obtained as shown below:
Of 853 people, 335 are Mexican. The proportion of juror is a Mexican American is p1 = 0.3927 and the sample size is n1 = 853
Of 853 people, 335 are Mexican; this implies that 518 are not Mexicans. The proportion of juror is a Mexican American is
p2 = 518/853 = 0.6073
The test statistic is,
z = p1- p2 / sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)
= (0.3927- 0.6072)/sqrt(0.3927(1-0.3927)/853 + 0.6072(1-0.6072)/853)
= -0.2145/0.0236
= -9.0889
p-value = 0.0001
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