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: Diet Barley Protein content of cow's milk 3.63 3.24 3.98 3.66 4.34 4.36 4.17 4.4 3.4 3.75 4.2 4.02 4.02 3.9 3.81 3.62 3.66 4.44 4.23 3.82 3.53 4.47 3.93 3.27 3.3 Barley+Lupins 3.38 3.8 3.8 Lupins 4.59 4.07 4.32 3.56 3.67 4.15 3.51 4.2 4.12 3.52 4.08 4.02 3.18 4.11 3.27 3.27 3.97 3.31 4.12 3.92 3.78 4 3.69 4.2 4.2 3.13 3.73 4.32 3.04 3.84 3.98 4.18 4.2 4.1 3.25 3.34 3.5 4.13 3.21 3.9 3.5 4.1 2.69 4.3 4.06 3.88 4 4.37 3.79 3.67 4.27 (a) What is the P-value from the ANOVA table? Round your answer to three decimal places (e.g. 98.765). P-value= +1 Answer *1: the absolute tolerance is +/-0.001 (b) Does diet affect the protein content of cow's milk? Use a = 0.05 and the P-value to make this inference. No, diet does not affect the protein content. Yes, diet affects the protein content. (c) Estimate variability due to random errors. Round your answer to three decimal places (e.g. 98.765). Answer *1: the absolute tolerance is +/-0.002