Chapter 10, Problem 56SE

Peanut Allergies In the study described in exercise $10.55$, researchers (Du Toits et al., 2015) also studied infants with eczema, egg allergies, or both who also had a preexisting sensitivity to peanut extract. These infants were also randomly assigned to either consume or avoid peanuts until 60 months of age. The numbers in each group developing a peanut allergy by 60 months of age are shown in the following table.

a. Compare the percentages in each group that developed a peanut allergy by age 60 months.

b. Test the hypothesis that treatment group and peanut allergy are associated using the chi-square statistic. Use a significance level of $0.05$.

c. Do a Fisher’s Exact Test for the data with the same significance level. Report the two-tailed $\text{p-value}$ and your conclusion. (Use technology to run the test.)

d. Compare the $\text{p-value}$ for parts b and

c. Which is more accurate? Explain.