Question

For a sample of 9 automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 10% of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to 10% of their original thickness. The results were as follows:

Car Rear Front
1 41.6 32.6
2 35.8 26.7
3 46.4 37.9
4 46.2 36.9
5 38.8 29.9
6 51.8 42.3
7 51.2 42.5
8 44.1 33.9
9 47.3 36.1
Find a 95% confidence interval for the difference in mean lifetime between the front and rear brake pads.

Answer 1

(8.734 ≤ μd ≤ 10.026)

Explanation:

Given the data:

Car Rear Front

1 41.6 32.6

2 35.8 26.7

3 46.4 37.9

4 46.2 36.9

5 38.8 29.9

6 51.8 42.3

7 51.2 42.5

8 44.1 33.9

9 47.3 36.1

Difference, d :

9, 9.1, 8.5, 9.3, 8.9, 9.5, 8.7, 10.2, 11.2

Mean difference, μd = Σd / n = 84.4 / 9 = 9.38

Standard deviation of difference, Sd = 0.84 (calculator)

The confidence interval :

μd ± margin of error

Margin of Error = Tcritical * Sd/√n

TCritical at 95%, df = 9-1 = 8

Tcritical = 2.306

Margin of Error = 2.306 * (0.84/√9) = 2.306*(0.84/3) = 0.64568

Lower boundary = 9.38 - 0.64568 = 8.73432

Upper boundary = 9.38 + 0.64568 = 10.02568

(8.734 ; 10.026)