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:

(a) Does diet affect the protein content of cow€™s milk? Draw comparative box plots and perform an analysis of variance. Use α = 0.05.

(b) Find the P-value of the test. Estimate the variability due to random error.

(c) Plot average protein content against diets and interpret the results.

(d) Analyze the residuals and comment on model adequacy.

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