3.7 Peanut Allergies. In the last 10 years, the prevalence of peanut allergies has doubled in Western countries. Is consumption or avoidance of peanuts in infants related to the development of peanut allergies in infants at risk? Subjects included infants between 4 and 11 months with severe eczema, egg allergy, or both, but who did not display a preexisting sensitivity to peanuts based on a skin-prick test. The infants were randomly assigned to either a treatment that avoided consuming pea- nut protein or a treatment in which at least 6 grams of peanut protein were con- sumed per week. The response was the presence or absence of peanut allergy at 60 months of age. In the avoidance group containing 263 infants, 36 had devel- oped a peanut allergy at 60 months of age, while in the consumption group contain- ing 266 infants, 5 had developed a peanut allergy.13 (a) Despite the large sample sizes in both treatments, why should we not use the large-sample confidence interval for these data? (b) The plus four method adds one success and one failure in each sample. What are the sample sizes and counts of successes after you do this? (c) Give the plus four 99% confidence interval for the difference in the prob- abilities of developing a peanut allergy for the avoidance and consumption treatments. What does your interval say about the comparison of these