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 $22,400. 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 99% 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? Round your answers to the nearest whole dollar.
$

(b) Construct the 99% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar.
< μ <

(c) Are you 99% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,400 and why?

Yes, because $22,400 is below the lower limit of the confidence interval for Vermont students. Yes, because $22,400 is above the lower limit of the confidence interval for Vermont students.     No, because $22,400 is above the lower limit of the confidence interval for Vermont students. No, because $22,400 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 less than 100. Because the sample size is greater than 30.     Because the margin of error is positive. Because the margin of error is less than 30.

    

    

Student	Debt
1	22364
2	26394
3	24280
4	25251
5	21725
6	24997
7	27366
8	25379
9	25203
10	21029
11	24335
12	24229
13	19302
14	22524
15	23700
16	24209
17	22081
18	26641
19	25532
20	19330
21	19565
22	27043
23	22194
24	25197
25	26658
26	21382
27	23098
28	22888
29	23827
30	23837
31	23599
32	26583
33	23151
34	23774
35	24845
36	26397
37	21421
38	22836
39	28462
40	25536

Answer 1