Question

For the following hypothesis test, where H₀: μ ≤ 10; vs. H_A: μ > 10, we reject H₀ at level of significance α and conclude that the true mean is greater than 10, when the true mean is really 14. Based on this information, we can state that we have:

Made a Type I error.

Made a Type II error.

Made a correct decision.

Increased the power of the test.

Answer 1

Solution:

Given hypothesis are:

H ₀ : µ ≤ 10; vs. H _A : µ> 10

Decision is: Reject H₀ at level of significance α and conclude that the true mean is greater than 10.

True condition is: the true mean is really 14, that means mean is greater than 10.

Definitions:

Type I Error = Reject H0, when H0 is true.

Type II Error = Fail to reject H0, when H0 is False.

Correct Decision: Reject H0, when H0 is False or Fail to reject H0, when H0 is True.

Since the true mean is really 14, that is mean is greater than 10 and we have rejected null hypothesis H ₀ : µ ≤ 10.

That means we have rejected null hypothesis H0, when H0 is False ( when H0 is not TRUE, that is alternative is TRUE).

Thus we have made correct decision.

Thus correct answer is:

Made a correct decision.