Question

An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 236 brakes using Compound 1 yields an average brake life of 48,737 miles. A sample of 190 brakes using Compound 2 yields an average brake life of 49,740 miles. Assume that the population standard deviation for Compound 1 is 4106 miles, while the population standard deviation for Compound 2 is 1104 miles. Determine the 80% 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 sox decimal places.

Step 3 of 3: Construct the 80% confidence interval. Round your answers to the nearest whole number.

Answer 1

The statistical software output for this problem is:

Two sample Z summary confidence interval:
?₁ : Mean of population 1 (Std. dev. = 4106)
?₂ : Mean of population 2 (Std. dev. = 1104)
?₁ - ?₂ : Difference between two means

80% confidence interval results:

Difference	n1	n2	Sample mean	Std. err.	L. limit	U. limit
?1 - ?2	236	190	-1003	279.02018	-1360.5787	-645.42125

Hence,

Step - 1: Point estimate = -1003

Step - 2: Margin of error = (-645.42125 + 1360.5787)/2 = 357.578725

Step - 3: 80% confidence interval: (-1361, -645)