# Question: A city police department is considering replacing the tires on

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.

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? 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?

(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.

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? 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?

**View Solution:**## Answer to relevant Questions

A botanist wishes to test the null hypothesis that the average diameter of the flowers of a particular plant is 9.6 cm. He decides to take a random sample of size n = 80 and accept the null hypothesis if the mean of the ...With reference to Example 12.1, what would have been the probabilities of type I and type II errors if the acceptance region had been x > 16 and the corresponding rejection region had been x ≤ 16? Example 12.1 Suppose that ...A single observation of a random variable having an exponential distribution is used to test the null hypothesis that the mean of the distribution is θ = 2 against the alternative that it is θ = 5. If the null hypothesis ...Show that the square of the expression for z in Exercise 13.12 equals So that the two tests are actually equivalent when the alternative hypothesis is θ1 ≠ θ2. The test described in Exercise 13.12, but not the one based ...With reference to Example 13.2, verify that the P-value corresponding to the observed value of the test statistic is 0.0808. Example 13.2 Suppose that 100 high-performance tires made by a certain manufacturer lasted on the ...Post your question