91影视

A sample survey of 870 people is recorded. Therefore, sample size $n=870$.

The sample proportion of Americans with Mexican ancestry is $\hat{p}=0.39$.

Among all the people in the grand jury duty, the proportion of Americans with Mexican ancestry is $0.791$.

The level of significance $伪=0.01$

The requirements for testing the claim for proportions are stated below.

1. Assume that 870 adults are selected randomly.
2. They are fixed of independent trails.
3. The requirements $np猢�5$and $nq猢�5$are satisfied as follows.

$$\begin{gathered} np=870脳0.791 \\ =688.17 \\ 猢�5 \end{gathered}$$

$$\begin{gathered} nq=870脳(1-0.791) \\ =181.83 \\ 猢�5 \end{gathered}$$

So, the three requirements for the z-test for proportions are satisfied.

Let p be the actual proportion of the selected people who are Americans of Mexican ancestry.

The hypotheses are as follows.

$H_0:p=0.791$(Null hypothesis)

$H_1:p<0.791$(Alternative hypothesis and original claim)

As the original claim contains a less-than symbol,it is a left-tailed test.

The sampling distribution of sample proportions can be approximated by the normal distribution.

The test statistic is given as follows.

$$\begin{gathered} z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}} \\ =\frac{0.39-0.791}{\sqrt{\frac{0.791脳(1-0.791)}{870}}} \\ =-29.0899 \end{gathered}$$

The test statistic value is -29.09.

This is a left-tailed test. So, the area of the critical region is an area of in the left tail. Referring to Table A-2 (standard normal table),the z-score value corresponding to 0.0100 corresponds to rows -2.3 and 0.03, which implies that its value is -2.33.

Thus, the critical value is -2.33.

Also, for the left-tailed test, the p-value is computed as 0.0001, corresponding to rows -3.5 and above.

Thus,

$$\begin{gathered} P-value=P\left(Z<-29.09\right) \\ =0.0001 \end{gathered}$$

The decision rule states the following:

If the test statistic value is lesser than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

In terms of p-value, reject the null hypothesis if the p-value is lesser than the level of significance. Otherwise, fail to reject the null hypothesis.

In this scenario, 0.0001 is lesser than 0.01. Hence, reject the null hypothesis.

As we reject the null hypothesis, there is sufficient evidence to support the claim that the population proportion is lesser than 79.1%.

Therefore, the process is biased against the Americans of Mexican ancestry, and the jury selection system appears to be biased.