Chapter 9.1, Problem 19E

(a)

To determine

The hypotheses for the significance test to check whether the average response time has decreased or not.

Answer to Problem 19E

For null hypothesis $H_0$ mean response time is equal to 6.7, for alternative hypothesis $H_a$ mean response time is less than 6.7.

Explanation of Solution

Given Information:

Population mean $\overline{x}=125.7$

Number of sample $n=45$

By the null hypothesis,mean response time is equal to 6.7 minutes.

Thus, $H_0:\mu =6.7$ minutes.

By the alternative hypothesis mean response time is less than 6.7 minutes.

Thus, $H_a:\mu <6.7$ minutes.

Hence, for null hypothesis $H_0$ mean response time is equal to 6.7, for alternative hypothesis $H_a$ mean response time is less than 6.7.

(b)

To determine

Explain Type I error and Type II error and their consequences.

Answer to Problem 19E

In Type I error the response time has improved and the training does not have to be improved, but actually the training needs to improve.

In Type II error instead of the response time, training should be improve, but in reality the training should not be improved.

Explanation of Solution

In Type I error, when the null hypotheses is true than $H_o$ is rejected.

Thus, the mean response time is equal to 6.7 minutes, but the test indicates that the mean response time is less.

Hence, the response time has improved and the training does not have to be improved, but actually the training needs to improve.

In Type II error,when the null hypotheses is true than rejection of $H_o$ also failed.

Thus, the mean response time is less than 6.7 minutes, while the test indicates that it is not less.

Hence, instead of the response time, training should be improve, but in reality the training should not be improved.

(c)

To determine

Explain which type of error is more serious.

Answer to Problem 19E

Type I error is more serious.

Explanation of Solution

The training has improved in Type II error but in Type I error, the training is not improved but in reality training needs to be improved in Type I error.

Hence,Type I error is more serious.