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. 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: p = 0.392
h₁: p > 0.392
(type integers or decimals. do not round.)
(c) what would it mean to make a type i error?
the president dropdown the hypothesis that the proportion of students who earn a bachelors degree within six years is dropdown input when, in fact, the proportion is dropdown input
(type integers or decimals. do not round.)

Explanation:

A Type I error occurs when we reject the null hypothesis \(H_0\) when it is actually true. In this context, the null hypothesis \(H_0:p = 0.392\) (where \(p\) is the proportion of students who earn a bachelor's degree within six years at the junior - college).

Answer:

The president rejects the hypothesis that the proportion of students who earn a bachelor's degree within six years is equal to \(0.392\) when, in fact, the proportion is equal to \(0.392\).