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 $22,800. 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 95% 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 95% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar. < μ <   (c) Are you 95% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,800 and why? Yes, 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.    No, because $22,800 is above the lower limit of the confidence interval for Vermont students.No, because $22,800 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 margin of error is positive. Because the sample size is less than 100.     Because the margin of error is less than 30. Because the sample size is greater than 30. Student Debt    1 22511 2 26541 3 24427 4 25398 5 21872 6 25144 7 27513 8 25526 9 25350 10 21176 11 24482 12 24376 13 19449 14 22671 15 23847 16 24356 17 22228 18 26788 19 25679 20 19477 21 19712 22 27190 23 22341 24 25344 25 26805 26 21529 27 23245 28 23035 29 23974 30 23984 31 23746 32 26730 33 23298 34 23921 35 24992 36 26544 37 21568 38 22983 39 28609 40 25683 Additional Materials

Answer 1

a)
point estimate for the mean = 24101.1

b)

z value at 95% = 1.96

CI = 24101.1 +/- 1.96 *(2224.5240/sqrt(40))
= (23411.7129,24790.4871)

23412 < mu < 24790

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.