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

0.396

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.

​(a) State the hypotheses.

Upper H 0H0​:

muμ

▼

Upper H 1H1​:

muμ

equals=

​(Type integers or decimals. Do not​ round.)

Answer 1

a) As we are to test here, whether the proportion of students who enroll in her institution have a

lower completion rate than 0.396, the null and the alternate hypothesis here are given as:

b) Type I error is the probability of rejection of a true null hypothesis. Here it is defined as the probability of rejecting the null hypothesis and concluding that the proportion of students who enroll in her institution have a lower completion rate than 0.396 given that the true proportion of students who enroll in her institution have a completion rate of 0.396.

c) Type II error is the probability of not rejecting a false null hypothesis. Here it is defined as the probability of not rejecting the null hypothesis and concluding that the proportion of students who enroll in her institution have a completion rate of 0.396 given that the true proportion of students who enroll in her institution have a completion rate of lower than 0.396.