In a 2015 study reported in the New England Journal of Medicine, Du Toit et al. randomly assigned infants who were likely to develop a peanut allergy (as measured by having eczema, egg allergies, or both) to either consume or avoid peanuts until 60 months of age. The infants in this cohort did not previously show any preexisting sensitivity to peanut extract. 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 p-value and your conclusion. (Use technology to run the test.)

d. Compare the p-values for parts b and c. Which is more accurate? Explain.

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Treatment Group Peanut allergy at age 60 mos. Consume peanuts Avoid peanuts Yes 5 37 No 267 233