Question

An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 124 brakes using Compound 1 yields an average brake life of 40,704 miles. A sample of 163 brakes using Compound 2 yields an average brake life of 43,525 miles. Assume that the population standard deviation for Compound 1 is 2022 miles, while the population standard deviation for Compound 2 is 4792 miles. Determine the 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

Answer 1

Given that,

For Compound 1 :

For Compound 2 :

A 90% confidence level has significance level of 0.10 and critical value is,

The 90% confidence interval for the (μ1 - μ2) is

Therefore, the 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-3507, -2135) miles.