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

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 tills (the machine producing fills with the smaller variance being preferable). Let and be the till variances for machines produced by companies A and B. respectively. Now\' consider various tests of the null hypothesis samples of fills from the two machines and using the test statistic 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. The manager of the dairy A salesperson for company A A salesperson for company B

Solution

A)

The manager does not have any bias, so he wants a TWO TAILED AREA.

*******************

b)

For company A, it wants to prove that it has less variability, so, since it is in the numerator, it wants a LOWER TAILED AREA.

***********************

c)

For company B, it wants to prove that it has less variability, so, since it is in the denominator, it wants a UPPER TAILED AREA.