Problem 1 The eggprod dataset concerns an experiment where six pullets were placed into each of 12 pens. Four blocks were formed from groups of three pens based on location. Three treatments were applied. The number of eggs produced was recorded. library(faraway) data (eggprod) (a) Make plots which show the responses (eggs) according to treat and block, and comment. (5 pts) (b) Fit a fixed effects model for the number of eggs produced with the treatments and blocks as predictors. Determine the significance of the two predictors and perform a basic diagnostic check. (7 pts) (c) Fit a model for the number of eggs produced with the treatments as fixed effects and the blocks is random effects. (3 pts) . Find estimated treatment effect for each treatment level. (3 pts) . Compare two variance components. (3 pts) (d) Use the Kenward-Roger approximation for an F-test to check for differences between the treatments. How does the result compare to the fixed effects model result? (6 pts) (e) Perform the same test but using a bootstrap method. How do the results compare? (To do this, please use the for loop with set . seed (123) before you run the iterations to make a consistent dutcpme. (10 pts) (f) Test for the significance of the blocks using the function exactRLRT. Does the outcome agree with the fixed effects model result? (5 pted (g) Find how much the predicted block effects from the random effects model are shrunken compared to the estimated block effects from the fixed effects model. (7 pta)