Question

for students who first enrolled in two - year public institutions in a recent semester, the proportion who earned a bachelors degree within six years was 0.392. the president of a certain junior college believes that the proportion of students who enroll in her institution have a higher 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 ii error.
(a) state the null hypothesis in words. choose the correct answer below.
a. among students who enroll at the certain junior college, the completion rate is greater than 0.392
b. among students who enroll at the certain junior college, the completion rate is less than 0.392
c. among students who first enroll in two - year public institutions, the completion rate is 0.392
d. among students who enroll at the certain junior college, the completion rate is 0.392

Explanation:

• The null hypothesis ($H_0$) is a statement of no difference or no effect. In hypothesis testing for proportions, when comparing a specific institution (the certain junior college in this case) to a known proportion (0.392 for two - year public institutions), the null hypothesis assumes that the proportion at the specific institution is equal to the known proportion.
• Option A is incorrect as it is not specific about the institution. Option B is an alternative hypothesis (claim of a higher rate). Option C is also an alternative hypothesis (claim of a lower rate). Option D is about two - year public institutions in general, not the specific junior college.

Answer:

D. Among students who enroll at the certain junior college, the completion rate is 0.392