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. An article 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. (Use i = 1, 2, 3, and 4 respectively.) Sample
RegimenSample
SizeSample
MeanSample
SD
Breast milk1542.91.3
CO1743.11.5
SO843.71.2
SMO1443.91.2
(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?
___The distribution of polyunsaturated fat percentages for each of the four regimens must be uniform with equal variances.
___The distribution of polyunsaturated fat percentages for each of the four regimens must be normal with unequal variances.
___The distribution of polyunsaturated fat percentages for each of the four regimens must be normal with equal variances.
___The distribution of polyunsaturated fat percentages for each of the four regimens must be binomial with unequal variances.
(b) Carry out the test suggested in part (a). State the appropriate hypotheses.
H0: \mu1 = \mu2 = \mu3 = \mu4
Ha: all four \mui's are unequal
H0: \mu1 ? \mu2 ? \mu3 ? \mu4
Ha: at least two \mui's are equal
H0: \mu1 = \mu2 = \mu3 = \mu4
Ha: at least two \mu's are unequal
H0: \mu1 ? \mu2 ? \mu3 ? \mu4
Ha: all four \mui's are equal
Find the value of the test statistic in this test. (Round your answer to two decimal places.)
Show your work for the calculations of sum of squares, mean squares, and f-statistic. You work should be in the similar fashion to the work on the solution to practice exercise #6
f = ___
What can be said about the P-value?
___P-value > 0.100
___0.050 < P-value < 0.100
___ 0.010 < P-value < 0.050
___0.001 < P-value < 0.010
___P-value < 0.001
State the conclusion in the problem context. (Use \alpha = 0.05.) Justify your answer. In other words, explain briefly in terms of what basis you use to reach the conclusion.
___Reject H0. There are no significant differences in true average fat content.
___Fail to reject H0. There are significant differences in true average fat content between at least two groups.
___Reject H0. There are significant differences in true average fat content between at least two groups.
___Fail to reject H0. There are no significant differences in true average fat content.