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
state the alternative 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 first enroll in two - year public institutions, the completion rate is 0.392
c. among students who enroll at the certain junior college, the completion rate is 0.392
d. among students who enroll at the certain junior college, the completion rate is less than 0.392

Explanation:

• Null Hypothesis (\(H_0\)): The null hypothesis is a statement of no difference or no effect. In the context of hypothesis testing for proportions, it assumes that the proportion of students who earn a bachelor's degree within six years at the certain junior college is equal to the known proportion (\(p = 0.392\)) for two - year public institutions.
• Alternative Hypothesis (\(H_1\)): The alternative hypothesis is what we are trying to find evidence for. Since the president believes that the proportion of students who enroll in her institution have a higher completion rate, the alternative hypothesis is that the proportion is greater than \(0.392\).

Answer:

• (a) The null hypothesis in words: D. Among students who enroll at the certain junior college, the completion rate is \(0.392\)
• (a) The alternative hypothesis in words: B. Among students who enroll at the certain junior college, the completion rate is greater than \(0.392\)