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A sample of 35 two-year colleges in 2012-2013 had a mean tuition (for in-state undergraduate students)...

A sample of 35 two-year colleges in 2012-2013 had a mean tuition (for in-state undergraduate students) of $2918. The true standard deviation of the tuition for these schools is known to be $1079.

Calculate a 90% confidence interval for the average in-state tuition of all two-year colleges in 2012-2013.

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 2918

Population standard deviation = = 1079

Sample size = n = 35

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 1.645 * ( 1079/ $\sqrt$ 35 )

= 300.02

At 90% confidence interval estimate of the population mean is,

- E < < + E

2918 - 300.02 < < 2918 + 300.02

2617.98 < < 3218.02

A 90% confidence interval for the average in-state tuition of all two-year colleges in 2012-2013.is,

(2617.98 , 3218.02)

milcah answered 8 months ago

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