25. 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 longterm health. The article Essential Fat Requirements of Preterm Infants (Amer. J. Clin. Nutrit., 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:

Sample Sample Sample Regimen Size Mean SD Breast milk 8 43.0 1.5 CO 13 42.4 1.3 SO 17 43.1 1.2 SMO 14 43.5 1.2

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?