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In: Statistics and Probability

A simple random sample of 40 colleges and universities in the United States has a mean...

A simple random sample of 40 colleges and universities in the United States has a mean tuition of 17800 with a standard deviation of 11000. Construct a 95% confidence interval for the mean tuition for all colleges and universities in the United States. Round the answers to the nearest whole number.

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Expert Solution

Solution :

Given that,

Point estimate = sample mean = =17800

sample standard deviation = s =11000

sample size = n =40

Degrees of freedom = df = n -1= 40-1= 39

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,39 = 2.023

Margin of error = E = t/2,df * (s /n)

= 2.023*(11000/ 40)

Margin of error = E = 3519

The 95% confidence interval estimate of the population mean is,

- E < < + E

17800 - 3519 < < 17800 + 3519

14281 < < 21319

(14281,21319)

orchestra answered 2 years ago
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