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:

a. Construct a 99% confidence interval for the difference in mean lifetime between the front and rear brake pads.

b. An automotive engineer claims that the mean lifetime for rear brake pads is more than 10,000 miles more than the mean lifetime for front brake pads. Does the confidence interval contradict this claim?

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Car Rear Front - 41.2 32.5 2345678 35.8 26.5 46.6 35.6 46.9 36.2 39.2 29.8 51.5 40.9 51.0 40.7 46.0 34.5 9 47.3 36.5