Recently a university surveyed recent graduates of the Engli

Recently, a university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,500. The population standard deviation is $2,586. What is the 95% confidence interval for the mean salary of all graduates from the English Department?

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =25500 -1.96*2586/sqrt(400) = 25246.57

So the upper bound is

xbar + Z*s/vn =25500 +1.96*2586/sqrt(400)=25753.43

Answer: [$25,247, $25,753]