Question

The quality control manager at a light-bulb factory needs to estimate the mean life of a new type of light-bulb. The population standard deviation is assumed to be 65 hours. A random sample of 40 light-bulbs shows a sample mean life of 505 hours. Construct and explain a 95% confidence interval estimate of the population mean life of the new light-bulb.

what size sample would be needed to achieve a margin of error of 15 hours or less?

Answer 1

Solution :

Given that,

standard deviation = = 65

margin of error = E = 15

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 65) / 15)²

= 72.13 = 73

Sample size = 73