In a randomized, placebo controlled, double-blind study, 55 children (5 to 11 years old) who had an egg allergy were randomly assigned either oral immunotherapy or placebo. After 10 months of therapy, 22 of the 40 given the therapy passed the food challenge (did not react badly to eggs), and none of the children receiving the placebo passed the food challenge.
a. Find and compare the percentages in each sample that passed the food challenge.
b. Create a two-way table, and find and report the expected counts to see if any are below 5.
c. Test the hypothesis that treatment and children becoming desensitized are independent using a chi-square test. Use a significance level of 0.05.
d. Repeat the test, using Fisher's Exact Test. Assuming a two-sided hypothesis, report the p-value and conclusion from Fisher's Exact Test.
e. Which is more accurate, the p-value from the chi-square test or the p-value from Fisher's Exact Test? Why?