Question

For students who first enrolled in two year public instituitons in a recent semester, the proportion who earned a bachelor's degree within six years was 0.388. 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 & 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.

A.) State the hypotheses.

H0: _______

H1: _______

(Type integers or decimals. Do not round.).

B.) Which of the following is a Type I error?

1.) The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388.

2.) The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388.

3.) The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388

4.) The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388

C.) Which of the following Type II error

1.) The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388.

2.) The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388.

3.) The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388.

4.) The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388

Answer 1

(A) The null and alternative hypothesis for the test is:

; i.e., the true proportion of students who earn a bachelor's degree within six years is 0.388.

; proportion of students who earn a bachelor's degree within six years is greater than 0.388.

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(B) The correct option for Type I error is (2), i.e., The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is 0.388.

Type I error: When we reject the null hypothesis H₀ , when in reality the null hypothesis H₀ is TRUE. And the probability of committing the Type I error is know as , i.e., the level of significance.

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(C) The correct option for Type II error is (4), i.e., The president fails to reject the hypothesis that the proportion of students who earn a bachelor's degree within six years is 0.388, when, in fact, the proportion is greater than 0.388.

Type II error: When we Fail To Reject the null hypothesis H₀ , when in reality the null hypothesis H₀ is FALSE