Question

For a sample of 9 automobiles, the mileage (in 1000s of miles) at which the original front brake pads were worn to 9% of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to 9% of their original thickness. The results were as follows: Car Rear Front 1 40.6 32.5 2 35.4 27.1 3 46.6 35.6 4 47.3 35.6 5 38.7 30.3 6 51.2 41.1 7 50.6 40.7 8 45.9 34.3 9 47.2 36.5 Send data to Excel Part: 0 / 20 of 2 Parts Complete Part 1 of 2 (a) Construct a 99.5% confidence interval for the difference in mean lifetime between the front and rear brake pads. Let d represent the mileage of the rear pads minus the mileage of the front ones. Use tables to find the critical value and round the answers to at least two decimal places. A 99.5% confident that the mean difference in lifetime between front and rear brake pads is

Answer 1

CI =[- 4.588; 15.4]

Since the calculated value of t= 4.244 falls in the critical region so we reject H0 and conclude that we are not confident that the mean difference in lifetime between front and rear brake pads is 99.5%

Explanation:

The given data is

Car Rear Front d= rear- front

1 40.6 32.5 8.1

2 35.4 27.1 8.3

3 46.6 35.6 11

4 47.3 35.6 11.7

5 38.7 30.3 8.4

6 51.2 41.1 10.1

7 50.6 40.7 9.9

8 45.9 34.3 11.6

9 47.2 36.5 10.7

∑ = 89.8

Let the hypotheses be

H0: ud= 0 against the claim Ha: ud ≠0

The degrees of freedom = n-1= 9-1= 8

The significance level is 0.05

The test statistic is

t= d`/sd/√n

The critical region is ║t║≤ t (0.025,8) = ±2.306

Sd= 7.05434553

d`=∑d/n= 89.8/9= 9.978

Therefore

t= d`/ sd/√n

t= 9.978/ 7.054/√9

t= 4.244

1) Since the calculated value of t= 4.244 falls in the critical region so we reject H0 and conclude that we are not confident that the mean difference in lifetime between front and rear brake pads is 99.5%

2) the confidence interval for the difference of two samples can be calculated by

d ` ± td sd/√n

9.978 ±2.306* 7.054/√9

- 4.588; 15.4