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 $23,500. You take a random sample of 146 college students in the state of Vermont and find the mean debt is $24,500 with a standard deviation of $2,800. We want to construct a 90% confidence interval for the mean debt for all Vermont college students.

Answer 1

The confidence interval is (24116.3878,24883.6122).

Explanation:

We are given the following information in the question:

Population mean,
`\mu` = $23,500

Sample mean,
`\bar{x}` = $24,500

Sample standard deviation,s = $2,800

Sample size, n = 146

Confidence interval:

`\bar{x} \pm t_(critical)(s)/(√(n))`

Putting the values, we get,

`t_(critical)\text{ at}~\alpha_(0.05) = \pm 1.655436`

`24500 \pm 1.65543((2800)/(√(146)) ) = 24500 \pm 383.6122 = (24116.3878,24883.6122)`

The confidence interval is (24116.3878,24883.6122).