How often does the average driver have an accident? The Allstate Insurance Company determined the average number of years between accidents for drivers in a large number of U.S. cities. Following are the results for 32 cities east of the Mississippi River and 32 cities west of the Mississippi River.

a. Construct a 95% confidence interval for the difference in mean scores between western and eastern cities.

b. An insurance company executive claims that the mean number of years between accidents for western cities is 1.5 years greater than the mean for eastern cities. Does the confidence interval contradict this claim?

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East 10.2 9.5 11.2 11.4 9.8 10.0 11.6 10.7 9.5 9.0 7.2 11.5 7.7 9.0 8.9 8.4 6.8 5.3 8.0 8.8 9.0 10.0 9.7 11.6 7.9 9.9 10.5 11.9 10.9 8.6 6.7 9.6 West 9.5 7.9 13.4 12.6 9.7 8.2 14.0 7.1 10.2 9.4 10.8 9.5 7.5 9.1 8.4 7.6 7.4 7.7 7.1 11.9 10.2 11.9 7.7 7.0 10.0 8.1 11.5 8.4 9.6 9.5 9.9 11.5