Question

A random Sample of 79 light bulbs had a mean Iife of 400 hours with standard deviation of 28 hours. Construct 90% interval for the mean life of light bulbs

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 400

sample standard deviation = s = 28

sample size = n = 79

Degrees of freedom = df = n - 1 = 78

At 90% confidence level the t is ,

t _/2,df = t_0.05,78 = 1.665

Margin of error = E = t_/2,df * (s /n)

= 1.665 * (28 / 79)

= 5.245

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

- E < < + E

400 - 5.245 < < 400 + 5.245

394.755 < < 405.245

(394.755 , 405.245)