J. A research team studied Y, the protein production of a laboratory animal, and how Y was affected by the dose of medicine. The research team sought choose a dosage to that E(Y) was minimized. They used five doses of medicine: 0, 1, 2, 3, and 4. They randomly assigned 16 animals to dosage 0, 16 to dosage 1, 16 to dosage 2, 16 to dosage 3, and 16 to dosage 4. They observed that the average values of Y' at each dosage were Yo. = 98.6, y1. = 89.0, yz. = 66.4, ya. = 58.6, and y4. = 42.4, where y, was the average of the observations taken with dosage i = 0,1,2,3,4, respectively. They also observed that so = 2246, s? = 1628, s? = 2064, s? = 1482, and s = 2566, where s was the unbiased estimate of the variance for the observations taken with dosage i = 0,1,2,3,4 respectively. They correctly calculated that y.. = 71.0 and that the average s/ was 1,997.2. The total sum of squares was 183,048.24. They also correctly calculated the values of the four contrasts. The coefficients of the linear contrast were -2, -1,0,1,2;, and Azin = -142.8. The coefficients of the quadratic contrast were 2, -1, -2, -1,2; and Quad = 1.6. The coefficients of the cubic contrast were - 1,2,0, -2,1; and cubic = 4.6. The coefficients of the quartic contrast were 1, -4,6, -4,1; and AQuartic = -51.0.10. Test the null hypothesis that the linear model is adequate at the 0.10, 0.05, and 0.01 levels of significance. Report the analysis of variance table including the sum of squares due to lack of fit. What is the optimal dosage? This question is worth 50 points