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 provides the two estimates (in thousands of miles) for each tire.

a. Make a dotplot of the difference (Weight – Groove) in the estimate of wear for each tire using the two methods.

b. Describe what the graph reveals about whether the two methods give similar estimates of tire wear, on average.

c. Calculate the mean difference and the standard deviation of the differences. Interpret the mean difference.

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Tire Weight Groove Diff. Tire Weight Groove Diff. 1 45.9 35.7 10.2 9 30.4 23.1 7.3 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 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 2.