Suppose you are planning an experiment to test the effect of a certain drug treatment on drinking behavior in the rat. You will use a two-tailed t test to compare a treated group of rats against a control group; the observed variable will be Y = 1-hour water consumption after 23-hour deprivation. You have decided that, if the effect of the drug is to shift the population mean consumption by 2 ml or more, then you want to have at least an 80% chance of finding significant evidence for HA at the 5% significance level.
(a) Preliminary data indicate that the SD of Y under control conditions is approximately 2.5 ml. Using this as a guess of σ, determine how many rats you should have in each group.
(b) Suppose that, because the calculation of part (a) indicates a rather large number of rats, you consider modifying the experiment so as to reduce σ. You find that, by switching to a better supplier of rats and by improving lab procedures, you could cut the SD in half; however, the cost of each observation would be doubled. Would these measures be cost-effective; that is, would the modified experiment be less costly?