Question

For students who first enrolled in two year public institutions in a recent​semester, the proportion who earned a​ bachelor's degree within six years was 0.398 The president of a certain college believes that the proportion of students who enroll in her institution have a higher completion rate.

(A) Determine the null and alternative hypotheses.
(B) Explain what it would mean to make a Type I error.
(C) Explain what it would mean to make a Type II error.

Answer 1

A) Null hypothesis: H0: p = 0.398

Alternative hypothesis: H0: p < 0.398

B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.

C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.

Explanation:

A) The null and alternative hypotheses are given below:

From the given information, the claim is that the proportion of students who enroll in her institution have a lower completion rate. This is representing the alternative hypothesis. Thus

Null hypothesis:

H0: p = 0.398

Alternative hypothesis:

H0: p < 0.398

B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.

C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.