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)

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