Researcher Francisco Fuentes and his colleagues wanted to determine the most effective diet for reducing LDL cholesterol, the so-called "bad" cholesterol, among three diets: (1) a saturated-fat diet: 15% protein, 47% carbohydrates, and 38% fat (20% saturated fat, 12% monounsaturated fat, and 6% polyunsaturated fat); (2) the Mediterranean diet: 47% carbohydrates, and 38% fat (10% saturated fat, 22% monounsaturated fat, and 6% polyunsaturated fat); and (3) the US National Cholesterol Education Program or NCEP-1 Diet: 10% saturated fat, 12% monounsaturated fat, and 6% polyunsaturated fat. Participants in the study were shown to have the same levels of LDL cholesterol before the study and were randomly assigned to one of the three diets, or treatment groups. After 28 days, their LDL cholesterol levels were recorded.

The data in the following table are based on this study.

(a) Why is this study a completely randomized design?
(b) What is the response variable? What is the explanatory variable that is controlled and set at three levels?
(c) The participants were randomly assigned to one of three treatment groups. What is the purpose of randomization in this study?
(d) State the null and alternative hypotheses.
(e) Verify that the requirements to use the one-way ANOVA procedure are satisfied. Normal probability plots indicate that the sample data come from normal populations.
(f) Are the mean LDL cholesterol levels different at the a = 0.05 level of significance?
(g) Draw boxplots of the LDL cholesterol levels for the three groups to support the analytic results obtained in part (f).

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Mediterranean NCEP-1 Saturated Fat 245 218 56 131 125 184 125 100 116 123 173 78 166 223 101 160 140 144 104 177 158 130 151 101 193 196 145 83 138 135 300 224 118 243 208 144 75 140 149 145 150 130 240 211 71