Question

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

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.

(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.
?< μ < ?

(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.

Yes, because \$22,800 is below 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 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 22448 2 26478 3 24364 4 25335 5 21809 6 25081 7 27450 8 25463 9 25287 10 21113 11 24419 12 24313 13 19386 14 22608 15 23784 16 24293 17 22165 18 26725 19 25616 20 19414 21 19649 22 27127 23 22278 24 25281 25 26742 26 21466 27 23182 28 22972 29 23911 30 23921 31 23683 32 26667 33 23235 34 23858 35 24929 36 26481 37 21505 38 22920 39 28546 40 25620

a) The point estimate for the mean debt of all Vermont college students is

b)

c) No, because \$22,800 is below the lower limit of the confidence interval for Vermont students.

d) Because the sample size is greater than 30.

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