Question

The life in hours of a 75-watt light bulb is known to be normally distributed with σ = 27 hours. A random sample of 20 bulbs has a mean life of x Overscript bar EndScripts = 1015 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.

Answer 1

Margin of error = Width of confidence interval / 2

= 6 / 2

= 3

Sample size = (Z/2 * / E)²

= ( 1.96 * 27 / 3)²

= 311.17

n = 312 (Rounded up to nearest integer)