Question

# For students who first enrolled in two year public institutions in a recent​ semester, the proportion...

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 0.395.

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

 ​(a) Determine the null and alternative hypotheses. ​(b) Explain what it would mean to make a Type I error. ​(c) Explain what it would mean to make a Type II error. ​(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 0.3950.395​, ​when, in​ fact, the proportion is lessless than 0.3950.395. B. The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.3950.395​, ​when, in​ fact, the proportion is 0.3950.395. C. The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.3950.395​, ​when, in​ fact, the proportion is 0.3950.395. D. The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.3950.395​, ​when, in​ fact, the proportion is lessless than 0.3950.395. ​ (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 0.3950.395​, ​when, in​ fact, the proportion is 0.3950.395. B. The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.3950.395​, ​when, in​ fact, the proportion is 0.3950.395. C. The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.3950.395​, ​when, in​ fact, the proportion is lessless than 0.3950.395. D. The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is 0.3950.395​, ​when, in​ fact, the proportion is lessless than 0.3950.395.

a)

 null Hypothesis:               Ho: p = 0.395 alternate Hypothesis:    Ha: p < 0.395

b)

option B is correct

The president rejects the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is

0.395​, ​when, in​ fact, the proportion is 0.395.

c) option C

The president fails to reject the hypothesis that the proportion of students who earn a​ bachelor's degree within six years is

0.395 ​when, in​ fact, the proportion is less then 0.365

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