Question

Construct the 99.9% confidence interval for the difference P.-P, when x, = 16,1, - 26,X2 -23, and 2 - 55. Round the answers
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Answer #1
X1 16 X2 23
n1 26 n2 55
P1 0.61538 X1/n1 P2 0.418182 X2/n2
Pbar 0.48148 (X1+X2)/(n1+n2)
P1-P2 0.19720

99.9% Confidence interval:

99.9% CI alpha 0.001
Zc 3.290527 Use Z table
ME 0.382708 Zc*SQRT(P1(1-P1)/n1+P2(1-P2)/n2)
Upper 0.57991 (P1-P2) + Zc*SQRT(P1(1-P1)/n1+P2(1-P2)/n2)
Lower -0.1855 (P1-P2) - Zc*SQRT(P1(1-P1)/n1+P2(1-P2)/n2)

CI = (-0.186, 0.580)

-0.186 < P1-P2 < 0.580

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