A city police department is considering replacing the tires on its cars with a new brand tires. If μ₁ is the average number of miles that the old tires last and μ₂ is the average number of miles that the new tires will last, the null hypothesis to be tested is μ₁ = μ₂.

(a) What alternative hypothesis should the department use if it does not want to use the new tires unless they are definitely proved to give better mileage? In other words, the burden of proof is put on the new tires, and the old tires are to be kept unless the null hypothesis can be rejected.

(b) What alternative hypothesis should the department use if it is anxious to get the new tires unless they actually give poorer mileage than the old tires? Note that now the burden of proof is on the old tires, which will be kept only if the null hypothesis can be rejected.

(c) What alternative hypothesis should the department use so that rejection of the null hypothesis can lead either to keeping the old tires or to buying the new ones?