Paired tires Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained.

Both methods were used to estimate the total distance traveled by each tire. The table below provides the two estimates (in thousands of miles) for each tire.29

(a) Construct and interpret a 95% confidence interval for the mean difference m in the estimates from these two methods in the population of tires.

(b) Does your interval in part

(a) give convincing evidence of a difference in the two methods of estimating tire wear? Justify your answer.

Tire Weight Groove Diff. Tire Weight Groove Diff.

1 45.9 35.7 10.2 9 30.4 23.1 7.3 2 41.9 39.2 2.7 10 27.3 23.7 3.6 3 37.5 31.1 6.4 11 20.4 20.9 −0.5 4 33.4 28.1 5.3 12 24.5 16.1 8.4 5 31.0 24.0 7.0 13 20.9 19.9 1.0 6 30.5 28.7 1.8 14 18.9 15.2 3.7 7 30.9 25.9 5.0 15 13.7 11.5 2.2 8 31.9 23.3 8.6 16 11.4 11.2 0.2