Question

# The average student loan debt of a U.S. college student at the end of 4 years...

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

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.