Reconsider Exercise 13-15 in which the effect of different diets on the protein content of cow€™s milk was investigated. Suppose that the three diets reported were selected at random from a large number of diets. To simplify, delete the last two observations in the diets with n = 27 (to make equal sample sizes).
(a) How does this change the interpretation of the experiment?
(b) What is an appropriate statistical model for this experiment?
(c) Estimate the parameters of this model.

Exercise 13-15

In the book Analysis of Longitudinal Data, 2nd ed. (2002, Oxford University Press), by Diggle, Heagerty, Liang, and Zeger, the authors analyzed the effects of three diets on the protein content of cow€™s milk. The data shown here were collected after one week and include 25 cows on the barley diet and 27 cows each on the other two diets:

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Protein Content of Cow's Milk 3.66 4.36 4.17 4.34 4.32 4.07 4.59 Diet Barley 3.63 Barley + lupins 3.38 3.69 4.2 3.24 4.4 3.56 3.67 3.4 3.75 3.9 3.52 3.98 4.02 4.02 4.2 4.17 4.15 3.51 4.12 3.8 4.2 4.08 3.34 Lupins 3.04 3.98 3.13 4.32 4.2 4.1 3.25 3.31 3.73 3.84 4.18 Diet (continued) Barley Barley + lupins 4.02 Lupins 3.62 4.11 3.66 4.23 3.27 3.82 4.47 3.93 3.27 3.92 3.81 4.44 3.3 4.37 3.53 3.79 3.18 3.27 3.97 3.31 4.12 3.78 4 2.69 3.88 3.5 4.13 3.21 3.9 3.5 4.06 3.67 4.27 4.1 4.3 4