A team of automotive engineers want to compare the lifetimes of two brands of tire. They obtain samples of seven tires of each brand. On each of seven cars, they mount one tire of each brand on each front wheel. The cars are driven until only \(20 \%\) of the original tread remains. The distances, in miles, for each tire are presented in the following table. Can you conclude that there is a difference between the mean lifetimes of the two brands of tire?

a. State the appropriate null and alternative hypotheses.

b. Compute the value of the test statistic.

c. Find the \(P\)-value and state your conclusion.

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Car 123 2 4 567 Brand 1 36,925 45,300 36,240 32,100 37,210 48,360 38,200 Brand 2 34,318 42,280 35,500 31,950 38,015 47,800 33,215