Question

An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 259 brakes using Compound 1 yields an average brake life of 47,112 miles. A sample of 218 brakes using Compound 2 yields an average brake life of 30,864 miles. Assume that the population standard deviation for Compound 1 is 1681 miles, while the population standard deviation for Compound 2 is 1627 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: Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Step 3 of 3: Construct the 98%98% confidence interval. Round your answers to the nearest whole number.

Answer 1

Step - 1: Point estimate = 47112 - 30864 = 16248

Step - 2: For 98% confidence, z = 2.33

Hence,

Margin of error = = 353.207636

Step - 3: 98% CI:

(15895, 16601)