Among a sample of 65 students selected at random from one hi

Among a sample of 65 students selected at random from one high school, the mean number of siblings is 1.3 with a standard deviation of 1.1. Find a 95% confidence interval for the mean number of siblings for all students at this high school.

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 =1.3 -1.96*1.1/sqrt(65 ) =1.032581

So the upper bound is

xbar + Z*s/vn =1.3 +1.96*1.1/sqrt(65 ) =1.567419