In: Math
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.
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 = Z0.05 = 1.645
Margin of error = E = Z/2* ( /n)
= 1.645 * ( 1079/ 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)