Question

The charts show results of studies on four-year colleges in the United States. You want to portray your college in a positive light for an advertising campaign designed to attract high school students. You decide to use hypothesis tests to show that your college is better than the average in certain aspects. EXERCISES

1. What Would You Test? What claims could you test if you wanted to convince a student to come to your college? Suppose the student you are trying to convince is mainly concerned with (a) affordability, (b) having a good experience, and (c) graduating and starting a career. List one claim for each case. State the null and alternative hypotheses for each claim.

2. Choosing a Random Sample Classmates suggest conducting the following sampling techniques to test various claims. Determine whether the sample will be random. If not, suggest an alternative. (a) Survey all the students you have class with and ask about the average time they spend daily on different activities. (b) Randomly select former students from a list of recent graduates and ask whether they are employed. (c) Randomly select students from a directory, ask how much debt money they borrowed to pay for college this year, and multiply by four.

3. Supporting a Claim You want your test to support a positive claim about your college, not just fail to reject one. Should you state your claim so that the null hypothesis contains the claim or the alternate hypothesis contains the claim? Explain.

4. Testing a Claim You want to claim that students at your college graduate with an average debt of less than $25,000. A random sample of 40 recent graduates has a mean amount borrowed of $23,475 and a standard deviation of $8000. At a = 0.05, is there enough evidence to support your claim?

5. Testing a Claim You want to claim that your college has a freshmen retention rate of at least 80%. You take a random sample of 60 of last year’s freshmen and find that 54 of them still attend your college. At a = 0.05, is there enough evidence to reject your claim?

6. Conclusion Test one of the claims you listed in Exercise 1 and interpret the results. Discuss any limits of your sampling process.

College Success                                

Freshman retention rate   

                                                   73.9%

4-year graduation rate 5-year graduation rate

                39.8%

5-year graduation rate

              55.3%

6-year graduation rate

      59.6%

Recent graduate employment rate

94.4%

_______________________________________x

0              20           40         60             80        100

College Cost

Annual tuition, public, In-state

$9130

Annual tuition, public, Out-of-state       

$21,303

Annual tuition, private                 

                                                                                $33,635

Amount borrowed                        

                                                                $29,411

Need-based scholarship or grants

                      $14,719

________________________________________x

0               10,000                20,000                 30,000

                                Amount

Student Daily Life

Sleeping

8.8

Leisure and sports

4.0

Educational Activities

       3.5

Working

2.3

Traveling

1.4

Dining

1.0

Other

                  3.0

_____________________________________x

0              2             4             6            8             10

Average (in hours)

Answer 1

Note : Allowed to solve one question.

Solve question 4 and 5 in details.

4. Testing a Claim You want to claim that students at your college graduate with an average debt of less than $25,000. A random sample of 40 recent graduates has a mean amount borrowed of $23,475 and a standard deviation of $8000. At a = 0.05, is there enough evidence to support your claim?

Hence we conclude that there no enough evidence to support the claim that students at your college graduate with an average debt of less than $25,000

5. Testing a Claim You want to claim that your college has a freshmen retention rate of at least 80%. You take a random sample of 60 of last year’s freshmen and find that 54 of them still attend your college. At a = 0.05, is there enough evidence to reject your claim?

There is sufficient evidence to claim that your college has a freshmen retention rate of at least 80%