Student Debt – Vermont (Raw Data, Software Required): The average student loan d
ID: 3319429 • 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 $22,600. 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.
Yes, because $22,600 is below the lower limit of the confidence interval for Vermont students.
No, because $22,600 is below the lower limit of the confidence interval for Vermont students.
Yes, because $22,600 is above the lower limit of the confidence interval for Vermont students.
No, because $22,600 is above the lower limit of the confidence interval for Vermont students.
Because the sample size is less than 100.
Because the margin of error is less than 30.
Because the margin of error is positive.Because the sample size is greater than 30.
(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 95% 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 95% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,600 and why?
Yes, because $22,600 is below the lower limit of the confidence interval for Vermont students.
No, because $22,600 is below the lower limit of the confidence interval for Vermont students.
Yes, because $22,600 is above the lower limit of the confidence interval for Vermont students.
No, because $22,600 is above 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 margin of error is less than 30.
Because the margin of error is positive.Because the sample size is greater than 30.
Student Debt 1 22322 2 26352 3 24238 4 25209 5 21683 6 24955 7 27324 8 25337 9 25161 10 20987 11 24293 12 24187 13 19260 14 22482 15 23658 16 24167 17 22039 18 26599 19 25490 20 19288 21 19523 22 27001 23 22152 24 25155 25 26616 26 21340 27 23056 28 22846 29 23785 30 23795 31 23557 32 26541 33 23109 34 23732 35 24803 36 26355 37 21379 38 22794 39 28420 40 25494Explanation / Answer
The statistical software output for this problem is:
One sample T confidence interval:
: Mean of variable
95% confidence interval results:
Hence,
a) Point estimate for mean debt = $ 23912
b) 95% confidence interval:
($ 23201, $ 24624)
c) Yes, because $22,600 is below the lower limit of the confidence interval for Vermont students.
d) Because the sample size is greater than 30.
Variable Sample Mean Std. Err. DF L. Limit U. Limit Debt 23912.1 351.72812 39 23200.663 24623.537