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 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 180,125 persons eligible for jury duty, of whom 143,400 were Mexican Americans. Of the 874 people selected for jury duty, 334 were Mexican Americans. (a) What proportion of eligible voters were Mexican Americans? Let this value be po. (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 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

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.)

Conclusion

Reject the null hypothesis, there is significant evidence of a difference in proportions. Reject the null hypothesis, there is not significant evidence of a difference in proportions.     Fail to reject the null hypothesis, there is not significant evidence of a difference in proportions. Fail to reject the null hypothesis, there is significant evidence of a difference in proportions.

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

very different very similar     none of the above

z P-value

Explanation / Answer

a) Proportion of eligible voters that are Mexican American = 143400/180125 = 0.7961

b) The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.7961
HA : p 0.7961

Hypothesis test results:

Hence,

z = -30.37

P-value = 0.0000

Conclusion: Reject the null hypothesis, there is significant evidence that Mexican Americans are underrepresented on juries. Option A is correct.

c) Total number of persons who are non jurors = 180125 - 874 = 179251

Total number of Mexican Americans among non Jurors = 143400 - 334 = 143066

So,

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

Hence,

z = -30.45

P-value = 0.0000

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

Option A is correct.

Comparison: Very similar

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 334 874 0.38215103 0.013628144 -30.374567 <0.0001

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