Question

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

x1 = 35, n1 = 243, x2 = 36, n2 = 309, 99% confidence

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

(Use ascending order. Type an integer or decimal rounded to three decimal places as needed)

Answer 1

Here, , n1 = 243 , n2 = 309
p1cap = 0.144 , p2cap = 0.1165

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.144 * (1-0.144)/243 + 0.1165*(1-0.1165)/309)
SE = 0.029

For 0.99 CI, z-value = 2.58
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.144 - 0.1165 - 2.58*0.029, 0.144 - 0.1165 + 2.58*0.029)
CI = (-0.047 , 0.102)

The researchers are 99% confident the difference between the two population proportions, p1 - p2, is between -0.047 and 0.102.