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. 

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