Question Help In randomized, double-blind clinical trials of a new vaccine, monk

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Question Help In randomized, double-blind clinical trials of a new vaccine, monkeys 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, 111 of 711 subjects in the experimental group (group 1) experienced vomiting as a side effect. After the first dose 60 of 624 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, P1 -P2. Use x1-111, n1 711, x2 -60, and n2 624 The 90% confidence interval for p1-p2 is (1,1) (Use ascending order. Round to three decimal places as needed.)

Explanation / Answer

p1=111/711= 0.156
p2=60/624=0.096

p1-p2= 0.06
a=0.1, |Z(0.05)|=1.645 (check standard normal table)

SO 90% CI is
(p1-p2)±Z*[p1*(1-p1)/n1+p2*(1-p2)/n2]

--> (0.06)±1.645*sqrt(0.156*(1-0.156)/711+0.096*(1-0.096)/624)

--> ( 0.030, 0.089)

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