Question

The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $22,900. You take a random sample of 40 college students in the state of Vermont. The debt for these students is found in the table below. We want to construct a 90% confidence interval for the mean debt for all Vermont college students. You will need software to answer these questions. You should be able to copy and paste the data directly from the table into your software program.

(a) What is the point estimate for the mean debt of all Vermont college students?
$  

(b) Construct the 90% confidence interval for the mean debt of all Vermont college students.
< μ <   

(c) Are you 90% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,900 and why?

Yes, because $22,900 is below the lower limit of the confidence interval for Vermont students.No, because $22,900 is above the lower limit of the confidence interval for Vermont students.     Yes, because $22,900 is above the lower limit of the confidence interval for Vermont students.No, because $22,900 is below the lower limit of the confidence interval for Vermont students.

(d) We are never told whether or not the parent population is normally distributed. Why could we use the above method to find the confidence interval?

Because the sample size is greater than 30.Because the sample size is less than 100.     Because the margin of error is less than 30.Because the margin of error is positive.

    

    

Student	Debt
1	22469
2	26499
3	24385
4	25356
5	21830
6	25102
7	27471
8	25484
9	25308
10	21134
11	24440
12	24334
13	19407
14	22629
15	23805
16	24314
17	22186
18	26746
19	25637
20	19435
21	19670
22	27148
23	22299
24	25302
25	26763
26	21487
27	23203
28	22993
29	23932
30	23942
31	23704
32	26688
33	23256
34	23879
35	24950
36	26502
37	21526
38	22941
39	28567
40	25641

Answer 1

Following is the output of 90% confidence interval generated by excel;

(a)

The point estimate for the mean debt of all Vermont college students is 24059.10

(b)

The 90% confidence interval for the mean debt of all Vermont college students is

$23466.80 < μ < $24651.72

(c)

Yes, because $22,900 is below the lower limit of the confidence interval for Vermont students.

(d)

Because the sample size is greater than 30.