Question

Student Debt – Vermont (Raw Data, Software Required):
The average student loan debt of a U.S. college student at the end of 4 years of college is estimated to be about $22,800. 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.

Student	Debt
1	22448
2	26478
3	24364
4	25335
5	21809
6	25081
7	27450
8	25463
9	25287
10	21113
11	24419
12	24313
13	19386
14	22608
15	23784
16	24293
17	22165
18	26725
19	25616
20	19414
21	19649
22	27127
23	22278
24	25281
25	26742
26	21466
27	23182
28	22972
29	23911
30	23921
31	23683
32	26667
33	23235
34	23858
35	24929
36	26481
37	21505
38	22920
39	28546
40	25620

(a) What is the point estimate for the mean debt of all Vermont college students? Round your answers to the nearest whole dollar. $ (b) Construct the 90% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar. < μ < (c) Are you 90% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,800 and why? No, because $22,800 is below the lower limit of the confidence interval for Vermont students.No, because $22,800 is above the lower limit of the confidence interval for Vermont students.    Yes, because $22,800 is below the lower limit of the confidence interval for Vermont students.Yes, because $22,800 is above 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 margin of error is positive.Because the sample size is greater than 30.    Because the margin of error is less than 30.Because the sample size is less than 100.

Answer 1

The statistical software output for this problem is:

On the basis of above output:

a) Point estimate = 24038

b) 90% confidence interval:

23445 < μ < 24631

c) Yes, because $22,800 is below the lower limit of the confidence interval for Vermont students.

d) Because the sample size is greater than 30.