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 0.392. 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
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
(b) state the hypotheses symbolically
h₀
h₁
(type integers or decimals. do not round.)

Explanation:

Step1: Determine the null hypothesis

The null hypothesis \(H_0\) is a statement of no difference or equality. Here, it assumes that the proportion of students who earn a bachelor's degree within six years at the junior college is the same as the known proportion for two - year public institutions. So, \(H_0:p = 0.392\)

Step2: Determine the alternative hypothesis

The president believes the completion rate is higher. The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for. So, \(H_1:p>0.392\)

Answer:

\(H_0:p = 0.392\)
\(H_1:p>0.392\)