Tire manufacturers are often interested in comparing the wear patterns of their tires with that of the other competitors. One way of comparing the wear patterns is to look at both the mean tread life and the variability in wear based on the brand of the tire. Two different brands of tires were sampled. The number of miles until the tires were considered worn-out is given in Table 5.12.

a. Is there a difference in the mean tire life between the two different brands? Explain.

b. Find and interpret a \(95 \%\) confidence interval for the ratio of the variances for the two different brands of tires.

c. Is there a difference in the variability in the tire life between the two different brands? Explain.

d. What is the minimum difference in the mean wear mileage between the two brands of tires that can be found with the given sample size?

e. How big of a sample would be needed to find at least a 5,000-mile difference between the mean wear patterns for the two brands of tires?

Table 5.12

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Number of Miles Until Worn-out for Two Different Brands of Tires Brand 1 Brand 2 36,250 44,981 50,225 48,587 40,016 57,859 56,281 66,496 41,437 53,531 53,516 38,210 52,365 42,010 57,697 51,425 58,508 60,218 41,664 63,506 55,348 52,107 50,481 68,119 46,221 41,186 62,109 60,922 56,333 57,267 61,787 53,544 39,930 52,812 56,101 45,732