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 junior college believes that the proportion of students who enroll in her institution have a lower completion rate.

(a) State the null and alternative hypotheses in words
(b) State the null and alternative hypotheses symbolically.
(c) Explain what it would mean to make a Type I error.
(d) Explain what it would mean to make a Type Il error.

Answer 1

The null hypothesis states that the proportion of students who enroll in a junior college and earn a bachelor's degree within six years is equal to or greater than that of students in two-year public institutions. The alternative hypothesis states that the proportion is lower. Making a Type I error means rejecting the null hypothesis when it's actually true, while making a Type II error means failing to reject the null hypothesis when it's actually false.

Step-by-step explanation:

(a) Null Hypothesis: The proportion of students who enroll in the junior college and earn a bachelor's degree within six years is equal to or greater than the proportion for students in two-year public institutions.

Alternative Hypothesis: The proportion of students who enroll in the junior college and earn a bachelor's degree within six years is lower than the proportion for students in two-year public institutions.

(b) Null Hypothesis (symbolically): p ≥ 0.398
Alternative Hypothesis (symbolically): p < 0.398

(c) Type I Error: Making a Type I error would mean rejecting the null hypothesis when it is actually true. In this context, it would mean concluding that the proportion of students who enroll in the junior college and earn a bachelor's degree within six years is lower, when in fact it is not.

(d) Type II Error: Making a Type II error would mean failing to reject the null hypothesis when it is actually false. In this context, it would mean not concluding that the proportion of students who enroll in the junior college and earn a bachelor's degree within six years is lower, when in fact it is.