Homework Soursein randomized doubleblind clinical trials of a new vaccine c
in randomized, double-blind clinical trials of a new vaccine, children were randomly divided into two groups. subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. after the first dose, 104 of 738 subjects in the experimental group (group 1) experience vomiting as a side effect. after the first dose, 66 of 639 of the subjects in the control group (group 2) experienced vomiting as a side effect. construct a 90% confidence interval for the difference between the two population proportions
Solution
Getting p1^ and p2^,
p1^ = x1/n1 = 0.140921409
p2 = x2/n2 = 0.103286385
Also, the standard error of the difference is
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.017577941
For the 90% confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.05
z(alpha/2) = 1.644853627
lower bound = p1^ - p2^ - z(alpha/2) * sd = 0.008721885
upper bound = p1^ - p2^ + z(alpha/2) * sd = 0.066548164
Thus, the confidence interval is
( 0.009 , 0.067) [ANSWER]
