Question

For a sample of nine 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 are given in the following table.

Automobile	Front	Rear
1	32.8	40.9
2	26.6	35.2
3	35.6	46.1
4	36.4	46
5	29.2	39.9
6	40.9	51.7
7	40.9	51.6
8	34.8	46.1
9	36.6	47.3

Let μXμX represent the population mean for rear brake pads and let μYμY represent the population mean for front brake pads. Find a 95% confidence interval for the difference μD=μX−μYμD=μX−μY. Round the answers to three decimal places.

The 95% confidence interval for the difference in mean is: (___, ___)

Answer 1

Automobile	Front	Rear	Difference
1	32.8	40.9	-8.1
2	26.6	35.2	-8.6
3	35.6	46.1	-10.5
4	36.4	46	-9.6
5	29.2	39.9	-10.7
6	40.9	51.7	-10.8
7	40.9	51.6	-10.7
8	34.8	46.1	-11.3
9	36.6	47.3	-10.7
		Total	-91

Sample size = n = 9

Sample mean = = - 10.1111

Standard deviation = Sd = 1.0994

Level of confidence interval is

Degrees of freedom = n - 1 = 9 - 1 = 8

tc = 2.306 ( Using t table)

The 95% confidence interval for the difference in mean is:( - 10.956 , - 9.266)