Peanut allergy is becoming increasingly common in Western countries. A study enrolled infants with a diagnosed peanut sensitivity and randomly assigned them to either avoid or regularly consume peanuts until 60 months of age. At the end of the study, 18 of the 51 children who had avoided peanuts were still allergic to peanuts. In contrast, 5 of the 47 children who had regularly consumed peanuts were still allergic to peanuts.We want to run a test to see whether peanut allergy at 60 months is affected by the long-term consumption or avoidance of peanuts among children diagnosed in infancy with a peanut allergy.

a. Organize the study findings in a two-way table of counts. What are the proportions of children still allergic to peanuts at 60 months in the two feeding conditions?

b. Find the expected cell counts under the null hypothesis that there is no difference outcome between the two feeding conditions. Verify that the expected counts meet our guideline for use of the chi-square test.

c. Are the proportions of children still allergic to peanuts at 60 months significantly different for the two approaches? Obtain the testP-value and conclude in context.