Chapter 21, Problem 23E

(a)

To determine

To explain what is meant by the power of the test the regulators are conducting.

Explanation of Solution

It is given in the question that a clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Thus, the power of the test the regulators are conducting means that the probability of detecting a shop that is not meeting standards.

(b)

To determine

To explain will the power be greater if they test $20\text{ or 40}$ cars and why.

Answer to Problem 23E

The power would be greater if they test $40$ cars.

Explanation of Solution

It is given in the question that a clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Thus, the power would be greater if they test $40$ cars because if the sample size will increase then the power of the test will increase.

(c)

To determine

To explain will the power be greater if they use a $5\%\text{ or a 10\%}$ level of a significance and why.

Answer to Problem 23E

The power would be greater if they use a $10\%$ level of a significance.

Explanation of Solution

It is given in the question that a clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Thus, the power would be greater if they use a $10\%$ level of a significance because there is more chance to reject the null hypothesis.

(d)

To determine

To explain will the power be greater if the repair shop’s inspectors are only a little out of compliance or a lot and why.

Answer to Problem 23E

The power would be greater if the repair shop’s inspectors are only a lot out of compliance.

Explanation of Solution

It is given in the question that a clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Thus, the power would be greater if the repair shop’s inspectors are only a lot out of compliance because larger differences are much easier to detect.