Safety regulations state that roller coasters cannot operate safely in low tempe

Question

Safety regulations state that roller coasters cannot operate safely in low temperatures. Throughout the day, ride operators measure the temperature at several random locations along the track to verify that the temperature is above an established threshold value, allowing the ride to operate safely. The collected data is used to conduct a one-sample z-test of the null hypothesis that the mean temperature is warm against the alternative that the mean temperature is too low. 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 error in this context.

Type I error:

The temperature is too low to operate safely, and the ride is shut down.

The temperature is too low to operate safely, and the ride continues to operate.

The temperature is warm enough to operate safely, and the ride continues to operate.

The temperature is warm enough to operate safely, and the ride is shut down.

Type II error:

The temperature is too low to operate safely, and the ride is shut down.

The temperature is warm enough to operate safely, and the ride continues to operate.

The temperature is too low to operate safely, and the ride continues to operate.

The temperature is warm enough to operate safely, and the ride is shut down.

Explanation / Answer

If we reject null hypothesis then there was sufficient evidence to say that the temperature is too low to operate safely,

and the ride is shut down.

If actually the temperature is too low to operate safely then there was no error.

But if actual the temperature is warm enough to operate safely, and we decide the ride is shut down then Type I error occur. So the correct description of Type I error is

"The temperature is warm enough to operate safely, and the ride is shut down."

Type II error occur if we fail to reject null hypothesis but actually it is not true.

So in this case if actually the temperature is too low to operate safely, but we find from sample that it the temperature is warm enough to operate safely, then Type II error occur.

So answer is "

The temperature is too low to operate safely, and the ride continues to operate".

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