Question: In a clinical trial of a vaccine, 300,000 children were randomly divided into two groups. The subjects in group 1 (the experimental group) were given a vaccine while the subject in group 2 (the control group) were given the placebo. Of the 150,000 children in the experimental group, 25 developed the disease. Of the 150,000 children in the control group, 126 developed the disease.

Test the claim that the proportion of subjects in the experimental group who contracted the disease is less than the proportion of subject in the control group who contracted the disease at the a=0.1 level of significance. What is the result of this hypothesis test?

Construct a 99% confidence interval for the difference between the two population proportions, p¹-p²

The 99% confidence interval for p¹-p^{2 =}