Question

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, 114 of 722 subjects in the experimental group​ (group 1) experienced fever as a side effect. After the first​ dose, 71 of 609 of the subjects in the control group​ (group 2) experienced fever as a side effect. Construct a 99 ​% confidence interval for the difference between the two population​ proportions, p 1 minus p 2 . Use x 1 equals 114​, n 1 equals 722​, x 2 equals 71​, and n 2 equals 609 . The 99 ​% confidence interval for p 1 minus p 2 is ​(nothing ​,nothing ​). ​(Use ascending order. Round to three decimal places as​ needed.)

Answer 1

Values are given as,

x 1 = 114​	n 1 = 722	p1= (x1/n1) = (114/722) = 0.158
x 2 = 71	n 2 = 609	p2= (x2/n2) = (71/609) = 0.117

Z critical value of 99% = = 2.576

calculating 99% confidence interval:

Putting the values:

CI = 0.004 , 0.078

The 99% confidence interval : ( 0.004   0.078)