In randomized, double-blind clinical trials of a new vaccine, children were rand

Question

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, 113 of 705 subjects in the experimental group (group 1) experienced vomiting as a side effect. After the first dose, 65 of 631 of the subjects in the control group (group 2) experienced vomiting as a side effect. Construct a 99% confidence interval for the difference between the two population proportions, p_1 - p_2. Use x_1 = 113, n_1 = 705, x_2 = 65, and n_2 = 631. The 99% confidence interval for p_1 - p_2 is (Use ascending order. Round to three decimal places as needed.)

Explanation / Answer

p1 = 113/705 = 0.160284

p2 = 0.103011

pooled Proportion = (113+65)/(705+631) = 0.133234

Margin of error = 2.5758*Sqrt((0.133234*(1-0.133234)/705)+(0.133234*(1-0.133234)/631) = 0.04797

99% Interval

(0.160284-0.103011-0.04797, 0.160284-0.103011+0.04797)

= (0.009, 0.105)

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