Suppose a poultry scientist comes to you to help him set up an experiment. He wants to compare the effects of 3 different diets (treatments) on eggshell prop- erties. He has available 6 strains of chickens. Each chicken included in the experiment will be housed in a separate pen during the duration of the trial. He has 30 pens available which are arranged in stacks of 5 side-by-side (see diagram below).

 For each chicken, measurements are taken on 5 randomly selected eggs. (i) What kind of experimental design would you use? Give its parameters (that is, t,

b, etc.)? (ii) Give a suitable arrangement of the diets (A, B, C) to the chickens. (iii) For the design proposed in (ii) give an appropriate linear model and outline the ANOVA, giving sources of variation and d.f. (iv) Upon further questioning you find out that the height of the pen in the stack may have an effect on the outcome of the experiment (because of differences in the temperature). Would you change the arrangement of the treatments given in (ii)? If your answer is "no", give reasons for it; if your answer is "yes", give the new arrangement.

(v) For the new situation described in (iv) give an appropriate linear model and outline the ANOVA giving sources of variation and d.f.