A company that manufactures steel wires guarantees that the mean breaking strength (in kilonewtons) of the wires is greater than 50. They measure the strengths for a sample of wires and test Hv0 : u =50 versus Hv1 : u >50.

Question

If a Type I error is made, what conclusion will be drawn regarding the mean breaking strength?

The conclusion will be that the mean breaking strength is [blank] 50

Answer 1

If a Type I error is made in this hypothesis test, it means that the null hypothesis \( H_0: \mu = 50 \) is rejected when it is actually true. Therefore, the conclusion drawn will incorrectly indicate that the mean breaking strength is greater than 50 when, in fact, it is not.

So the conclusion will be that the mean breaking strength is greater than 50.

Answer 2

If a Type II error is made, what conclusion will be drawn regarding the mean breaking strength?

The conclusion will be that the mean breaking strength is [blank] 50 .

Answer 3

If a Type II error is made in this hypothesis test, it means that the null hypothesis \( H_0: \mu = 50 \) is not rejected when it is actually false (i.e., when the true mean breaking strength is actually greater than 50).

Therefore, the conclusion drawn will incorrectly suggest that the mean breaking strength is not greater than 50 when, in reality, it is.

So the conclusion will be that the mean breaking strength is not greater than 50.

Answer 4

This test uses a one-tailed alternative hypothesis. Explain why a one-tailed hypothesis is more appropriate than a two-tailed hypothesis in this situation.

With a one-tailed hypothesis, we can conclude that the mean breaking strength is [blank] 50. With a two-tailed hypothesis, we will not know whether the mean breaking strength is [blank] 50 .

Answer 5

A one-tailed hypothesis is more appropriate in this situation because the company's objective is specifically to test whether the mean breaking strength of the wires is greater than 50. They are only interested in one direction of effect: confirming that the mean strength exceeds 50 kilonewtons. This focus allows them to allocate more statistical power to detecting an increase in breaking strength, as a one-tailed test requires fewer samples to achieve the same level of significance compared to a two-tailed test.

With a one-tailed hypothesis, we can conclude that the mean breaking strength is greater than 50. With a two-tailed hypothesis, we will not know whether the mean breaking strength is greater than or less than 50.