Student Debt – Vermont (Raw Data, Software Required): The average student loan d
ID: 3259893 • 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 $22,800. 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 90% 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 $22,800 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. Yes, because $22,800 is below the lower limit of the confidence interval for Vermont students.Yes, because $22,800 is above the lower limit of the confidence interval for Vermont students.
Because the margin of error is positive.Because the sample size is greater than 30. Because the sample size is less than 100.Because the margin of error is less 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.
$
(b) Construct the 90% confidence interval for the mean debt of all Vermont college students. Round your answers to the nearest whole dollar.
< <
(c) Are you 90% confident that the mean debt of all Vermont college students is greater than the quoted national average of $22,800 and why?
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. Yes, because $22,800 is below the lower limit of the confidence interval for Vermont students.Yes, because $22,800 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 margin of error is positive.Because the sample size is greater than 30. Because the sample size is less than 100.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 25536Explanation / Answer
using minitab
Here we used sample data set and population standard deviation is not given . Also sample size is sufficiently
large( >= 30) so we can used one sample t confidence interval.
The command is Stat>>>Basic Statistics >>1 sample t...
click on sample in columns:
Select column in which Debt data present.
then click on Option select level of confidence = (1 - alpha) * 100 = (1 - 0.1)*100 = 90
Alternative " not equal"
Click on OK
Again Click on OK
We get the following output
MTB > Onet 'Debt';
SUBC> Confidence 90.
One-Sample T: Debt
Variable N Mean StDev SE Mean 90% CI
Debt 40 23954 2225 352 (23361, 24547)
a) The point estimate for the mean debt of all Vermont college students is sample mean 23954
b) The 90% confidence interval for the mean debt of all Vermont college students is (23361, 24547)
c) the answer of this part is Yes, because $22,800 < lower limit of 90% cnfidence interval that is less than 23361
so correct choice is "Yes, 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.
We use the above method to find the confidence interval because if the sample size greater than 30 then by central
limit theorem sampling distribution of sample mean is approximately normally distributed.