A tire manufacturer believes that a new tire it is introducing (Brand A) will have longer wear than the comparable tire (Brand B) sold by its main competitor. To get evidence to back up its claim in planned advertising, the manufacturer conducts a study. On each of four cars it uses a tire of Brand A on the left front and a tire of Brand B on the right front. The response is the number of thousands of miles until a tire wears out, according to a tread marking on the tire. The sample mean response is 50 for Brand A and 40 for Brand B.
a. Show a pattern of four pairs of observations with these means for which you think Brand A would be judged better according to statistical inference. You do not need to actually conduct the inference. (What affects the value of the test statistic, other than the sample means and n?)
b. How could the design of this study be improved?