An experiment is being planned to compare the effects of several diets on the weight gain of beef cattle, measured over a 140-day test period.20 In order to have enough precision to compare the diets, it is desired that the standard error of the mean for each diet should not exceed 5 kg.
(a) If the population standard deviation of weight gain is guessed to be about 20 kg on any of the diets, how many cattle should be put on each diet in order to achieve a sufficiently small standard error?
(b) If the guess of the standard deviation is doubled, to 40 kg, does the required number of cattle double? Explain.