CASE STUDY II. Vitamin May Affect the Weight Gain? A scientist wants to see if the type of four vitamin supplements (A, B, C, D) affects the weight gain (y in grams) of laboratory animals. The experiment was conducted in a completely randomized design with five separately caged animals for each treatment. Since the caloric intake (z in calories/10) will differ among animals and influence y, she wants to take this variable into account in the analysis. The data are given in the following table: Supplement Y I A 48 35 A 67 44 A 78 44 A 69 51 A 53 47 Supplement B B B B B y * 65 40 9 33 49 45 37 73 53 37 63 42 Supplement y I 79 51 52 41 63 47 65 47 67 48 00000 C C C Supplement Y I D 59 53 D 50 52 D 59 52 D 42 51 D 34 43 Let the significance level = 0.05. For each of the following questions, include the necessary out- put/plots/numbers to answer the questions and give a complete commentary on the results, written in report style: (a) Identify the following in terms of the above study. Be as specific as possible: Experimental unit(s) Population(s) Sample(s) Variables identify which are response(s), and which are explanatory and classify each as quantitative or categorical. Factor(s) and their levels. What are the treatments and how many are there? Is this study experimental or observational? Justify. Is the design balanced or unbalanced? Justify.