Question

Suppose we wish to test the null hypothesis mu is less than or equal to 47 versus the alternative hypothesis mu is greater than 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?
A. We have made a Type I error.
B. We have made a Type Il error.
C. We have made a correct decision.
D. None of the above are correct.

Answer 1

Answer:

C. We have made a correct decision

Step-by-step explanation:

Hypotheses are:

$H_{0}$: mu is less than or equal to 47

$H_{a}$: mu is greater than 47

Type I error happens when we reject the null hypothesis but the null hypothesis was true

Type II error happens when we fail to reject the null hypothesis but the null hypothesis was wrong.

In this example we concluded that mu is greater than 47, thus we reject the null hypothesis. Since true mean is 52, this conclusion is true. We have made a correct decision