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 181,825 persons eligible for jury duty, of whom 143,500 were Mexican Americans. Of the 880 people selected for jury duty, 338 were Mexican Americans.
(a) What proportion of eligible voters were Mexican Americans?
Let this value be p_{o}. (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 p̂ 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 α = 0.01. Round your test statistic to
two decimal places and your P-value to four decimal
places.)
z | |
P-value |
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 p_{1} be the
probability that a randomly selected juror is a Mexican American,
and let p_{2} be the probability that a randomly
selected nonjuror is a Mexican American. Find the z
statistic and its P-value. (Use α = 0.01. Round
your test statistic to two decimal places and your P-value
to four decimal places.)
z | |
P-value |
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 differentvery similar
none of the above
Castaneda v. Partida is an important court case in which statistical methods were used as part...
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...
Can you please answer this question with detail? 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...
Please show all the work and as much detail as possible!! Question 3 (20 pts In a court case reviewed by the Supreme Court 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 181,535 persons eligible for jury duty, of whom 143, 611 were Mexican Americans. Of the 870 people selected for jury duty, 339 were Mexican Americans. a. What proportion...
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