Question

A random sample of 104 light bulbs had a mean life of 543 hours. The lifetimes of this particular light bulb is know to have a standard deviation of 26 hours Construct a 90% confidence interval for the mean life, μ, of all light bulbs of this type. Provide the lower limit of the confidence interval for your answer.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 543

sample standard deviation = s = 26

sample size = n = 104

Degrees of freedom = df = n - 1 = 104 - 1 = 103

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,103 = 1.660

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

= 1.660* (26 / 104)

= 4.232

The 90% confidence interval estimate of the population mean is,

- E < < + E

543 - 4.232 < < 543 + 4.232

538.768 < < 547.232

Lower limit = 538.768