Question

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The process standard deviation is known to be 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours. Set up a 95% confidence interval estimate of the true population mean life of light bulbs in this shipment. Interpret your confidence interval.

Answer 1

Solution :

Given that,

= 350

= 100

n = 64

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

Margin of error = E = Z_/2* ( /n)

= 1.96 * (100 / 64)

= 24.5

At 95% confidence interval estimate of the population mean is,

- E < < + E

350 - 24.5 < < 350 + 24.5

325.5 < < 374.5

(325.5 , 374.5)