It is known that at a certain prestigious university, only 20% of applicants are offered admission. A college preparatory company claims that it has a program that increases the probability that an applicant to this university will gain admission. A consumer watchdog organization decides to test this claim with a hypothesis test on p, the proportion of potential applicants to the university who would be offered admission after completing this company's preparatory program.

1. Which of the following is the appropriate null hypothesis for this test?

a)H0:p= 0.20

b)H0:p >0.20

c)H0:p <0.20

2. Which of the following is the appropriate alternative hypothesis for this test? (Hint: This is thepreparatory company's claim.)

a)HA:p= 0.20

b)HA:p >0.20

c)HA:p <0.20

As part of this test, a sample is taken of n= 100 students who complete the preparatory program and apply to the university. (Assume that this can be viewed as a random sample of all potential users of the program.) Let p be the proportion of this sample who are offered admission to the university.

3. If the null hypothesis is correct, what are the mean, p, and the standard deviation,p, of the distribution of p values? (Write your answers in decimal form, accurate to three decimal places.)

4. Suppose that x= 25 of then= 100 applicants in this sample are offered admission to the university after completing the preparatory program. What is the appropriate conclusion that the consumer watchdog group should reach (using a significance level of= 0.05)?

a) They conclude that p is actually equal to 0.20

.b) They conclude that p is actually equal to 0.25.

c) They conclude that p is something larger than 0.20, without specifying what that value is.

d) They conclude that there is not enough evidence to support the company's claim.