The options for the 3 boxes at the bottom are for the first...

The options for the 3 boxes at the bottom are: for the first box; a) Do not reject or b) Reject. For the second box; a) is, or b) is not. For the third box; a) less than b) greater than c) not different from d) different from . Census data for a certain county show that 20% of the adult residents are Hispanic. Suppose 76 people are called for jury duty and only 13 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain. Write appropriate hypotheses. Ho: HA: The test statistic is z = (Round to two decimal places as needed. The P-value is (Round to three decimal places as needed.) State your conclusion assuming a P-value smaller than 0.05 is significant the null hypothesis. There sufficient evidence to conclude that the proportion of Hispanics in the jury pool is the proportion of Hispanics in the population.

Transcript

00:01 For this problem, we are told that 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.

00:09 For the period of time at issue, there were 181 ,535 persons eligible for jury duty, of whom 143 ,611 were mexican americans.

00:21 Of the 870 people selected for jury duty, 339 were mexican americans.

00:29 In part a, we are asked, what proportion of eligible jurors were mexican americans? and we are to denote this value by p.

00:36 Not.

00:37 So that would be, let's see here.

00:40 That would be 143 -611, divided by 181 -535.

00:46 So i'll get the numerical value here, round it.

00:49 So about 79%.

00:51 So p -0 is about 0 .79.

00:57 For part b, we're asked to let p be the probability that a randomly select juror is a mexican -american.

01:04 The null hypothesis to be tested is h -0, or is rather that p -0 equals p -not.

01:10 We're asked to find the value of p -hat, the sample proportion for this problem, to compute the z -statistic and estimate the p -value.

01:18 So, p -hat is going to be equal to, let's see here, 339, over 870, which gives us a result here of about approximately 0 .39.

01:39 Then our z score is going to be equal to p hat 0 .39 minus p .9, minus p .9, divided by the square root of p .0 .0 .79 times 1 minus p .0 over n.

01:58 And n was 870 .7 .000.

02:00 And n was 870.

02:00 So our z score, i'll just calculate this out here, 0 .39 minus 0 .79, divided by the square root of 0 .79 times 1 minus 0 .79 over 870.

02:16 So, wowza.

02:18 Our z score is negative, it's about negative 28 .97.

02:25 So we can reasonably estimate the p value as being approximately zero because of, how many standard deviations away, or essentially because of how large that z score is, p is very close to zero.

02:42 So we would reject the null hypothesis.

02:48 Then, for part c, whereas to reformulate the problem is a two -sample problem, where we wish to compare the proportion of mexican -americans among those selected as jurors with the proportion of mexican -american, pardon me, mexican -americans among those not selected as jurors...

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