1. A completely randomized experiment investigates the effects of increasing nitrogen (N) and copper (Cu) in the diet of chickens. Feed conversion ratio (FCR) is observed on n = 4 chickens for each of four treatment combinations(diets], with sample means and variances below. You should be able to complete these problems without software. (a) (3 pts) Write a factorial effects model for the 16 observed FCR measurements which assumes that, for a given diet, FCR is normally distributed, with variance of that is constant across diets. Be sure to include the model, the ranges of the subscripts, and the assumptions of the model. (b) (1 pt) Estimate the simple effect of increasing copper when N = 25. (c) (1 pt) Estimate the simple effect of increasing copper when N = 45 (d) (1 pt) Estimate the difference in the simple effects of increasing copper across levels of Nitrogen. (e) (4 pts) Using significance level a: .05, test the hypothesis that the simple effects of copper are constant across levels of nitrogen. State the null and alternative hypotheses, the test statistic, the rejection criterion, and your conclusion. (1 pt) Report the smallest level of significance at which the difference between simple copper effects across levels of nitrogen may be declared significant. (1 pt) Report a contrast sum of squares associated with the contrast tested in part (d). (3 pts) Estimate the simple effect of increasing N when Cu = 100. Report a standard error and a 95% confidence interval for the effect. In light of this interval, can you declare the observed effect "significant\" at level of significance or = .05? (i) (3 pts) Estimate the main effect of increasing Cu. Give the F -ratio for a test of no effect, along with degrees of freedom. (j) (2 pts) Reportthe contrast sums ofsquares for the main effect of copper and the main effect of nitrogen. (k) (3 pts) Obtain an ANOVA table which partitions the variability between the four treatments into meaningful components. (1) (1 pt) It turns out that a control was also run (with n = 4), without any added Cu or N, The mean FCR was yo = 131. The observed contrast of this mean with the average of the others is 5: 131 (1/4)(133 + 130 + 146 + 127] = 3. Compute 55(diet), the diet sum of squares (on df = 5 1 = 4) from a one-way analysis of variance using all five diets