A city police car is considering replacing the tires on its cars with a new bran

Question

A city police car is considering replacing the tires on its cars with a new brand of tires. If 1 is the average number of miles that the old tires last and 2 is the average number of miles that the new tires will last, the null hypothesis to be tested

isH0 :1 =2.

(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 to 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?

Explanation / Answer

a)

H1 : miu 1 is not equal to miu 2

b)

H1 : miu 1 is less than miu 2

c)

H1 : miu 1 is greater than miu 2

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