Student Debt – Vermont (Raw Data, Software Required): The average student loan d
ID: 3173079 • Letter: S
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 $22,500. 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.
No, because $22,500 is below the lower limit of the confidence interval for Vermont students.
Yes, because $22,500 is above the lower limit of the confidence interval for Vermont students.
No, because $22,500 is above the lower limit of the confidence interval for Vermont students.
Yes, because $22,500 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 less than 30.
Because the margin of error is positive.
(a) What is the point estimate for the mean debt of all Vermont college students? Round your answers to the nearest whole dollar.
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(b) Construct the 99% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar.
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(c) Are you 99% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,500 and why?
No, because $22,500 is below the lower limit of the confidence interval for Vermont students.
Yes, because $22,500 is above the lower limit of the confidence interval for Vermont students.
No, because $22,500 is above the lower limit of the confidence interval for Vermont students.
Yes, because $22,500 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 less than 30.
Because the margin of error is positive.
Student Debt 1 22490 2 26520 3 24406 4 25377 5 21851 6 25123 7 27492 8 25505 9 25329 10 21155 11 24461 12 24355 13 19428 14 22650 15 23826 16 24335 17 22207 18 26767 19 25658 20 19456 21 19691 22 27169 23 22320 24 25323 25 26784 26 21508 27 23224 28 23014 29 23953 30 23963 31 23725 32 26709 33 23277 34 23900 35 24971 36 26523 37 21547 38 22962 39 28588 40 25662Explanation / Answer
from above
a) point estimate of mean =24080.1
b)for 99% CI, and 39 df ; value of t=2.7079
hence confidence interval =mean +/- t*std error =23127.651 ; 25032.549
c) Yes, because $22,500 is below the lower limit of the confidence interval for Vermont students.
d)Because the sample size is greater than 30.
X 22490.000 26520.000 24406.000 25377.000 21851.000 25123.000 27492.000 25505.000 25329.000 21155.000 24461.000 24355.000 19428.000 22650.000 23826.000 24335.000 22207.000 26767.000 25658.000 19456.000 19691.000 27169.000 22320.000 25323.000 26784.000 21508.000 23224.000 23014.000 23953.000 23963.000 23725.000 26709.000 23277.000 23900.000 24971.000 26523.000 21547.000 22962.000 28588.000 25662.000 mean(X) 24080.100 std deviation(S) 2224.524 std error =S/(n)1/2 351.728