Chapter PVI, Problem 30RE

(a)

To determine

To explain is the percentage of speeding tickets issued to blacks unusually high compared to registrations.

Answer to Problem 30RE

There is sufficient evidence to support the claim that the percentage of spending tickets issued to blacks is unusually high compared with the state’s registration information.

Explanation of Solution

It is given in the question that a newspaper report in August raised the issue of racial bias in the issuance of speeding tickets. Thus, to find out any test for proportion we will use the calculator $\text{TI}-89$ . Then select $5:1-$ PropZTest from the STAT TESTSmenu. Specify the hypothesized proportion. Enter the observed value of x . Specify the sample size. Indicate what kind of test you want: one-tail lower tail, two-tail, or one-tail upper tail. Specify whether to calculate the result or draw the result. This is an upper tail test and the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p=0.16\\ H_a:p>0.16\end{array}$

Also, we know that,

  $\begin{array}{l}p=0.25\\ n=324\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}z=4.42\\ P=0\end{array}$

As we know that if the P-value is less than or equal to the significance level then the null hypothesis is rejected, so we have,

  $P<0.05\Rightarrow \text{Reject }{H}_0$

Thus, we conclude that there is sufficient evidence to support the claim that the percentage of spending tickets issued to blacks is unusually high compared with the state’s registration information.

(b)

To determine

To explain does this suggest that racial profiling may be present.

Answer to Problem 30RE

No, this does not suggest that racial profiling may be present.

Explanation of Solution

It is given in the question that a newspaper report in August raised the issue of racial bias in the issuance of speeding tickets. And there is sufficient evidence to support the claim that the percentage of spending tickets issued to blacks is unusually high compared with the state’s registration information. Thus, no, this does not suggest that racial profiling may be present because it is possible that other variables influence the fact that Blacks receive more speeding tickets such as income, intelligence, age, etc.

(c)

To determine

To explain what other statistics would you like to know about this situation.

Explanation of Solution

It is given in the question that a newspaper report in August raised the issue of racial bias in the issuance of speeding tickets. And there is sufficient evidence to support the claim that the percentage of spending tickets issued to blacks is unusually high compared with the state’s registration information. So, the other statistics we would like to know about this situation are income, intelligence, age, proportion of blacks on the highway, etc.