Question

Safety regulations state that roller coasters cannot operate safely in heavy rains. Throughout the day, ride operators measure the rainfall at several random locations along the track to verify that the rainfall is below an established threshold value. allowing the ride to operate safely. The collected data is used to conduct a one-sample 2-test of the null hypothesis that the mean rainfall is minimal against the alternative that the mean rainfall is too heavy. If the null hypothesis is rejected in favor of the alternative, the ride is shut down due to unsafe conditions. Choose the correct description of a type I error and a type II crror in this context. Type I error: a. The rainfall is minimal enough to operate safely, and the ride is shut down. b. The rainfall is minimal enough to operate safely, and the ride continues to operate. c. The rainfall is too heavy to operate safely, and the ride continues to operate, d. The rainfall is too heavy to operate safely, and the ride is shut down. Type II error: a. The rainfall is minimal enough to operate safely, and the ride is shut down. b. The rainfall is minimal enough to operate safely, and the ride continues to operate. c. The rainfall is too heavy to operate safely, and the ride is shut down. d. The rainfall is too heavy to operate safely, and the ride continues to operate.

Answer 1

Answer:

Type I error:

a. The rainfall is minimal enough to operate safely, and the ride is shut down.

Type II error:

d. The rainfall is too heavy to operate safely, and the ride continues to operate.

Step-by-step explanation:

In this case:

The null hypothesis (H0) states that mean rainfall is minimal

The alternative hypothesis (H1) states that mean rainfall is heavy.

A type I error occurs if one rejects the null hypothesis when it is actually true.

In this case; if the rainfall is minimal enough to operate safely and the ride is shut down is an example of Type I error because the null hypothesis is true and it is rejected.

A type II error occurs if one does not reject the null hypothesis when it is false, that is one accept the null hypothesis when it is false.

In this case; the null hypothesis is false and it is accepted is an example of type II error. So, the rainfall is too heavy to operate safely (means null hypothesis is false) and the ride continues to operate (means the null hypothesis is accepted when it is false).