Chapter 20, Problem 26E

To determine

To explain does this apparent underrepresentation of Hispanics all into question the fairness of the jury selection system.

Answer to Problem 26E

We fail to reject that Hispanics represented in the jury pool is $10\%$ of the general population.

Explanation of Solution

It is given in the question that census data for a certain county shows that $19\%$ of the adult residents are Hispanic. Thus, the null hypothesis states that the rate is equal to $19\%$ . And the alternative hypothesis states that the rate is less than $19\%$ . So, we define hypothesis as:

  $\begin{array}{l}{H}_0:p=0.19\\ H_a:p<0.19\end{array}$

Thus, let us check the appropriate conditions and assumptions for inference to proceed further to test hypothesis as:

Random condition: It is satisfied as we assumed that the sample was randomly selected from the population.

Independent condition: It is satisfied as we can assume that the sample is independent.

  $10\%$ condition: It is satisfied as the sample is less than $10\%$ of all population.

Success/failure condition: It is satisfied because both are greater than ten as,

  $\begin{array}{l}np=0.19(72)>10\\ n(1-p)=0.81(72)>10\end{array}$

Thus, all the conditions are satisfied. Thus, for this first we have to select $5:1-\text{PropZInt}$ from the STAT TESTS menu. Then, enter the observed count and sample size for the sample. Then we will indicate what kind of test we want: one-tail lower tail, two-tail, or one-tail upper tail. Then, we will specify whether to calculate the result or draw the result. Hence we have,

  $\begin{array}{l}x=9\\ n=72\\ c=0.95=95\%\end{array}$

So, by putting the values above by using the calculator we will get the result as,

The value of z-statistics and the P-value will be then,

  $\begin{array}{l}z=-1.41\\ P-\text{value}=0.079\end{array}$

And as we know if the P-value is smaller than the significance level, then reject the null hypothesis, so, we have,

  $P>0.05\Rightarrow \text{ Fail to Reject }{H}_0$

Thus, we can conclude that we fail to reject that Hispanics represented in the jury pool is $10\%$ of the general population.