Measurements of the heights of a random sample of 200 male s

Measurements of the heights of a random sample of 200 male students at XYZ University showed a mean of 67.5 inches and a standard deviation of 2.5 inches. Find a 95% confidence interval for estimating the mean height of the students.

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=67.5 -1.96*2.5/sqrt(200) =67.15352

So the upper bound is

xbar + Z*s/vn=67.5 +1.96*2.5/sqrt(200) =67.84648