Question

An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 260 brakes using Compound 1 yields an average brake life of 32,023 miles. A sample of 297 brakes using Compound 2 yields an average brake life of 39,570 miles. Assume that the population standard deviation for Compound 1 is 2395 miles, while the population standard deviation for Compound 2 is 1673 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 six decimal places.

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

Answer #1

1) = 32023 - 39570 = -7547

2) At 80% confidence interval the critical value is
z_{0.1} = 1.28

Margin of error = z_{0.1} *

= 1.28 *

= 227.125668

3) The 80% confidence interval is

() +/- ME

= -7547 +/- 227.125668

= -7774.125668, -7319.874332

= -7774, -7320

=

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