A rancher is interested in determining if the average daily gain in weight of calves depends on the bull that sired the calf. Consider the following two situations: Scenario A: The rancher has only five bulls. The five bulls are mated with randomly selected cows, and the average daily gains in weight by the calves produced by the matings are recorded. Scenario B: The rancher has hundreds of bulls and randomly selects five bulls for inclusion in the study. The five bulls are mated with randomly selected cows, and the average daily gains in weight by the calves produced by the matings are recorded.
The data are given here.

a. Write an appropriate linear statistical model for both scenario A and scenario B, identifying all the terms in the models.
b. State the null and alternative hypotheses for testing for a bull effect for each of the two scenarios.

Bull Bull2 Bull3 Bull Bull5 1.20 1.16 1.39 1.36 1.39 1.22 17 83 1.12 1.31 .75 .96 108 1.22 1.02 1.05 1.10 97 108 1.16 1.00 1.15 1.03 1.12 98