Question

An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 121 brakes using Compound 1 yields an average brake life of 39,122 miles. A sample of 163 brakes using Compound 2 yields an average brake life of 48,271 miles. Assume that the population standard deviation for Compound 1 is 3175 miles, while the population standard deviation for Compound 2 is 1335 miles. Determine the 98% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

Step 1 of 3: Find the point estimate for the true difference between the population means.

Step 2 of 3: Find the margin of error of a confidence interval for the difference between the two population means. Round to 6 decimals.

Step 3 of 3: Construct the 98% confidence interval. Round to 2 decimals.

Answer 1

The statistical software output for this problem is:

Hence,

Step - 1: point estimate = -9149

Step - 2: Margin of error = (-8903.3144 + 9394.6856)/2 = 601.706740

Step - 3: Lower limit = -9394.69

Upper limit = -8903.31