P. Noakes et al. researched the effects of fatty acids found in oily fish on lowering the risk of allergic disease in the article "Increased Intake of Oily Fish in Pregnancy: Effects on Neonatal Immune Responses and on Clinical Outcomes in Infants at 6 Mo." (American Journal of Clinical Nutrition, Vol. 95, No. 2, pp. 395-404). Pregnant women were randomly assigned to continue their habitual diet (control group), which was low in oily fish, or to consume two portions of salmon per week (treatment group). Their infants were clinically evaluated at 6 months of age and the frequency of many different symptoms was recorded. Of the 37 infants in the control group, 12 had symptoms of dry skin; and of the 45 infants in the experimental group, 14 had symptoms of dry skin. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in the proportions of infants who have symptoms of dry skin at 6 months between those whose mothers continue their habitual diet and those whose mothers consume two portions of salmon per week?
a. Use the two-proportions z-test (Procedure 12.3 on page 564) to
perform the required hypothesis test.
b. Use the chi-square homogeneity test to perform the required hypothesis test.
c. Compare your results in parts (a) and (b).
d. Explain what principle is being illustrated.