Question

Construct a confidence interval for p1 - p2 at the given level of confidence.

x1 = 364, n1 = 542, x2 = 422, n2 = 574, 90% confidence

The researchers are (BLANK)% confident the difference between the two population proportions, p1 - p2, is between

(BLANK) and (BLANK).

Answer #1

Here, , n1 = 542 , n2 = 574

p1cap = 0.6716 , p2cap = 0.7352

Standard Error, sigma(p1cap - p2cap),

SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)

SE = sqrt(0.6716 * (1-0.6716)/542 + 0.7352*(1-0.7352)/574)

SE = 0.0273

For 0.9 CI, z-value = 1.64

Confidence Interval,

CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)

CI = (0.6716 - 0.7352 - 1.64*0.0273, 0.6716 - 0.7352 +
1.64*0.0273)

CI = (-0.1084 , -0.0188)

The researchers are 90% confident the difference between the two
population proportions, p1 - p2, is between -0.1084 and
-0.0188

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