Chapter 9.1, Problem 22E

(a)

To determine

The hypotheses for the significance test of mean systolic pressure to check whether the person seek medical attention or not.

Answer to Problem 22E

For null hypothesis $H_0$ mean systolic pressure is equal to 130, for alternative hypothesis $H_a$ proportion is more than 130.

Explanation of Solution

Given Information:

  $\text{Estimated}\text{mean}\text{systolic}\text{blood}\text{pressure}\left(\mu \right)=130$.

By the null hypothesis,mean systolic pressureis equal to 130.

Thus, $H_0:\mu =130$

By the alternative hypothesis mean systolic pressure is more than 130.

Thus, $H_a:\mu >130$

Hence, for null hypothesis $H_0$ mean systolic pressure is equal to 130, for alternative hypothesis $H_a$ proportion is more than 130.

(b)

To determine

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

Answer to Problem 22E

In Type I error the mean systolic pressure is equal to 130 but the test indicates that the mean systolic pressure is more.

In Type II error mean systolic pressure is more than 130 but the test indicates that the mean systolic pressure is equal to 130.

Explanation of Solution

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

The mean systolic pressure is equal to 130but the test indicates that the mean systolic pressure is more.

Hence, the consequence is that they have high blood pressure and took action against high blood pressure but in reality they do not have high blood pressure.

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

The mean systolic pressure is more than 130 but the test indicates that the mean systolic pressure is equal to 130.

Hence, the consequence is that they have normal blood pressure and did not take action against high blood pressure but in reality they have high blood pressure and action should be taken.

(c)

To determine

Explain which type of error is more serious.

Answer to Problem 22E

Type II error is more serious.

Explanation of Solution

Since, there is no action taken against the high blood pressure as a result the individual could be die which is more serious.

Hence, type II error is more serious.