Question

# Student Debt – Vermont (Raw Data, Software Required): The average student loan debt of a U.S....

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

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