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 0.391. The president of a certain college believes that the proportion of students who enroll in her institution have a lowerlower completion rate.

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(b) Which of the following is a Type I​ error?

A.

The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is 0.391.

B.

The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is lessless than 0.391.

C.

The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is lessless than 0.391.

D.

The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is 0.391.

​

(c) Which of the following is a Type II​ error?

A.

The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is lessless than 0.391.

B.

The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is lessless than 0.391.

C.

The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is 0.391.

D.

The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is 0.391.

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Answer 1

ANSWER:

For students who first enrolled in two year public institutions in a recent​ semester:

(a) Determine the null and alternative hypothesis:

we have to obtained the null and alternative hypothesis is,

NULL HYPOTHESIS : p = 0.391.

and , ALTERNATIVE HYPOTHESIS : p > 0.391.

(b)  Which of the following is a Type I​ error.

We have to obtained the mean to to make type I error is ,

Here,

TYPE I error: The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is 0.391.

​Therefore ,

OPTION (D) is correct answer .

(c)  Which of the following is a Type II​ error;

We have to obtained the mean to make a type II error is ,

Here,

TYPE II error: The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.391​, ​when, in​ fact, the proportion is 0.391.

Therefore ,

OPTION ( B) is correct answer .