In randomized double-blind clinical trials of a new vaccine, infants were random

Question

In randomized double-blind clinical trials of a new vaccine, infants 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, 112 of 724 subjects in the experimental group (group 1) experienced fever as a side effect. After the first dose, 57 of 648 of the subjects in the control group (group 2) experienced fever as a side effect. Construct a 95% confidence interval for the difference between the two population proportions, p_1 -p_2. Use x_1 = 112, n_1 = 724, x_2 = 57, and n_2 = 648. The 95% confidence interval for p_1 - p_2 is (Use ascending order. Round to three decimal places as needed.)

Explanation / Answer

CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
No. of chances( X1 )=112
No.Of Observed (n1)=724
P1= X1/n1=0.155
Proportion 2
No. of chances(X2)=57
No.Of Observed (n2)=648
P2= X2/n2=0.088
C.I = (0.155-0.088) ±Z a/2 * Sqrt( (0.155*0.845/724) + (0.088*0.912/648) )
=(0.155-0.088) ± 1.96* Sqrt(0)
=0.067-0.034,0.067+0.034
=[0.033,0.101]

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