The manager of a dairy is in the market for a new

Chapter 10, Problem 83E

(choose chapter or problem)

Problem 83E

The manager of a dairy is in the market for a new bottle-filling machine and is considering machines manufactured by companies A and B. If ruggedness, cost, and convenience are comparable in the two machines, the deciding factor will be the variability of fills (the machine producing fills with the smaller variance being preferable). Let σ 2 1 and σ 2 2 be the fill variances for machines produced by companies A and B, respectively. Now consider various tests of the null hypothesis H0 : σ 2 1 = σ 2 2 . Obtaining samples of fills from the two machines and using the test statistic S2 1 / S2 2, we could set up as the rejection region an upper-tail area, a lower-tail area, or a two-tailed area of the F distribution, depending on the interests to be served. Identify the type of rejection region that would be most favored by the following persons, and explain why.

a The manager of the dairy

b A salesperson for company A

c A salesperson for company B