Question

A paper was reporting on the lifetime of a certain type of boiler. The average lifetime, based on 25 samples, was reported as 12 years. The paper also reported a p-value of 0.0088 to support the claim that this boiler’s average lifetime is less than 15 years. He, however, neglected to report the standard deviation of the boiler lifetime.a. What is the standard deviation of the boiler lifetime?b. Find a 95% confidence interval for the boiler lifetime?

Answer 1

a) We are given here the p-value as 0.0088

From standard normal tables, we have:

P( Z < -2.374 ) = 0.0088

Therefore, we have here:

Therefore 6.3184 is the required standard deviation here.

b) From standard normal tables, we have:

P( -1.96 < Z < 1.96 ) = 0.95

Therefore the confidence interval here is computed as:

This is the required confidence interval for the boiler lifetime mean.