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