Dravet syndrome is a complex childhood epilepsy disorder. Researchers Devinsky et al., conducted a double-blind placebo-controlled trial to determine the efficacy of the drub cannabiliol on reducing seizures in children with Dravet syndrome. One hundred twenty children with this syndrome were randomly assigned to receive either the drug or a placebo. Researchers then recorded the percentage in each group who saw at least a 50% reduction in seizure frequency. Of the 60 children assigned to the drug group, 43% saw this reduction in seizure frequency; of the 60 children assigned to the placebo group, 27% saw this reduction. 

a. Using a significance level of 0.05, do we have evidence the drug is effective in reducing seizures? You may use a chi-square test of homogeneity or a two-proportion z-test.

b. Suppose the sample sizes were doubled for each group and that the rates of seizure reduction remained the same. Repeat the test, reporting the new p-value and conclusion.

c. Explain the difference in the results between parts a and b.