Question

Suppose we wish to test the null hypothesis H0: μ ≤47 versus H1: μ > 47. What will result if we conclude thatthe mean is greater than 47 when its true value really is 52?

a. We have made a Type I error.
b. We have made a Type II error.
c. We have made a correct decision
d.None of the above are correct.

Answer 1

To test the null hypothesis H0: μ ≤47 versus H1: μ > 47, if we conclude that the mean is greater than 47 when its true value really is 52, we have made a Type I error.

Step-by-step explanation:

To test the null hypothesis H0: μ ≤47 versus H1: μ > 47, we need to consider two possible outcomes:

1. If we conclude that the mean is greater than 47 when its true value really is 52, then we have made a Type I error. This means that we have incorrectly rejected the null hypothesis and concluded that the mean is greater than 47, even though it is not.
2. If we conclude that the mean is not greater than 47 when its true value really is 52, then we have made a correct decision. This means that we have correctly failed to reject the null hypothesis and concluded that the mean is not greater than 47.

Therefore, the correct answer is d.None of the above are correct.