Suppose that we wanted the total width of the twosided confi

Suppose that we wanted the total width of the two-sided confidence interval on mean life to be six hours at 95% confidence. What sample size should be used? Round up the answer to the nearest integer.

1) The life in hours of a 75-watt light bulb is known to be normally distributed with ? = 23 hours. A random sample of 20 bulbs has a mean life of X = 1017 hours Suppose that we wanted the total width of the two-sided confidence interval on mean life to be six hours at 95% confidence. What sample size should be used? Round up the answer to the nearest integer.

Solution

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

E=6/2=3

So n=(Z*s/E)^2

=(1.96*23/3)^2

=225.8007

Take n=226