Refer to Exercise 9.20. Explain what each of the following would mean.

a. Type I error

b. Type II error

c. Correct decision

Now suppose that the results of carrying out the hypothesis test lead to rejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean post-work heart rate of casting workers

d. equals the normal resting heart rate of 72 bpm.

e. exceeds the normal resting heart rate of 72 bpm.

$H_0$The mean post-work heart rate of casting workers exceeds the normal resting heart rate of 72 (bpm).

$H_0:\mu =72bpm$

$H_a$: The mean post-work heart rate of casting workers exceeds the normal resting heart rate

exceeds 72 (bpm).

Versus,

$H_a:\mu >72bpm$

The type I error is defined as rejecting a null hypothesis when it is true, according to the definition. While it is true that the mean post-work heart rate of casting workers is equal to the normal resting heart rate of 72 (bpm), the sampling results lead to the conclusion that the mean post-work heart rate of casting workers exceeds the normal resting heart rate of 72 (bpm), resulting in the null hypothesis being rejected.

When the null hypothesis (H) is untrue, the type II error is defined as failing to reject it. If $\mu =72bpm$is not to be rejected, a type II error occurs, but the sample data fail to infer that the mean post-work heart rate of casting workers is equal to the typical resting heart rate of 72. (bpm).

If neither the true null hypothesis nor the false null hypothesis is rejected, the decision is correct. In this case, the mean post-work heart rate of casting workers is equal to the normal resting heart rate of 72 (bpm), and the sampling results do not lead to rejection, so the correct decision is; or the mean post-work heart rate of casting workers exceeds the normal resting heart rate of 72 (bpm), and the sampling results lead to the rejection of the null hypothesis of 72 bpm.

Here the mean post-work heart rate of casting workers equals to the normal resting heart rate of 72 (bpm), and the results of a hypothesis test lead to rejection of the null hypothesis. We need to classify the decision as an error type or a correct decision.

As a sampling result we obtain the mean post-work heart rate of casting workers equals to the normal resting heart rate of 72 (bpm), and we are rejecting the null hypothesis that the mean post-work heart rate of casting workers exceeds to the normal resting heart rate of 72 (bpm). that is the true null hypothesis rejected, So we are committing type 1 error.

Mean post-work heart rate of casting workers exceeds to the normal resting heart rate of 72 (bpm), and the results of a hypothesis test lead to rejection of the null hypothesis. We need to classify the decision as an error type or a correct decision.

We are not rejecting the null hypothesis of $\mu =16.7months$, where we obtain as a sampling result that mean length of imprisonment for motor-vehicle-theft offenders in differs from national mean of 16.7 months. Therefore, our decision is a correct decision.