Question

**Student Debt – Vermont:** 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 141 college students in the state of Vermont and find the mean
debt is $23,500 with a standard deviation of $2,800. You want to
construct a 90% confidence interval for the mean debt for all
Vermont college students.

(a) What is the point estimate for the mean debt of all Vermont
college students?

$

(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 $22,500 and
why?

Yes, because $22,500 is below the lower limit of the confidence interval for Vermont students.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.

(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 positive. Because the margin of error is less than 30.Because the sample size is greater than 30.

Additional Materials

Answer #1

(a)

Point estimate = $23,500

(b)

We need to construct the 90% confidence interval for the population mean μ. The following information is provided:

Sample Mean = | 23500 |

Sample Standard Deviation (s) = | 2800 |

Sample Size (n) = | 141 |

The critical value for α=0.1 and df=n−1=140 degrees of freedom is . The corresponding confidence interval is computed as shown below:

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.

**Let me know in
the comments if anything is not clear. I will reply ASAP! Please do
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