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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.

Respuesta :

Answer:

The confidence interval is (24116.3878,24883.6122).

Step-by-step explanation:

We are given the following information in the question:

Population mean, [tex]\mu[/tex] = $23,500

Sample mean,[tex]\bar{x}[/tex] = $24,500

Sample standard deviation,s = $2,800

Sample size, n =  146

Confidence interval:

[tex]\bar{x} \pm t_{critical}\frac{s}{\sqrt{n}}[/tex]  

Putting the values, we get,

[tex]t_{critical}\text{ at}~\alpha_{0.05} = \pm 1.655436[/tex]

[tex]24500 \pm 1.65543(\frac{2800}{\sqrt{146}} ) = 24500 \pm 383.6122 = (24116.3878,24883.6122)[/tex]

The confidence interval is (24116.3878,24883.6122).

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