Lipids provide much of the dietary energy in the bodies of infants and young children. There is a growing interest in the quality of the dietary lipid supply during infancy as a major determinant of growth, visual and neural development, and long-term health. The article "Essential Fat Requirements of Preterm Infants" (Amer. J. of Clinical Nutrition, 2000: 245S-250S) reported the following data on total polyunsaturated fats (%) for infants who were randomized to four different feeding regimens: breast milk, corn-oil-based formula, soy-oil-based formula, or soy-and-marine-oil-based formula:

a. What assumptions must be made about the four total polyunsaturated fat distributions before carrying out a single-factor ANOVA to decide whether there are any differences in true average fat content?
b. Carry out the test suggested in part (a). What can be said about the P-value?

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Sample Size Sample Mean Sample SD Regimen Breast milk SO 43.0 42.4 43.1 13 17 14 1.3 1.2 1.2 SMO