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
(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 rejects the hypothesis that the proportion of students who earn a bachelors degree within six years is equal to 0.392 when, in fact, the proportion is equal to 0.392
(type integers or decimals. do not round.)
(d) what would it mean to make a type ii error?
the president the hypothesis that the proportion of students who earn a bachelors degree within six years is when, in fact, the proportion is
(type integers or decimals. do not round.)

Explanation:

A Type II error occurs when we fail to reject the null hypothesis \(H_0\) even though the alternative hypothesis \(H_1\) is true. In this context, the null hypothesis \(H_0:p = 0.392\) (the proportion of students who earn a bachelor's degree within six years is \(0.392\)) and the alternative hypothesis \(H_1:p>0.392\) (the proportion is higher).

Answer:

The president fails to reject 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 greater than \(0.392\).