Question

Construct the indicated confidence interval for the difference between population proportions p1

-p2. Assume that the samples are independent and that they have been randomly selected.
x₁ = 30, n₁ = 65 and x2 = 47, n2 = 76; Construct a 95% confidence interval for the difference
between population proportions P1 - P2-
OPTIONS:
A) 0.268 < P1 - P2 < 0.655
B) -0.320 < P1 - P2 < 0.006
C) -0.351 < P1 - P2 < 0.655
D) 0.299 < P1 - P2 < 0.624

Answer 1

D) 0.299 < P1 - P2 < 0.624

To construct the 95% confidence interval for the difference between two population proportions, P1 - P2, you can use the formula:

CI = (p1 - p2) ± 1.96 * sqrt(p1 * (1 - p1) / n1 + p2 * (1 - p2) / n2)

where p1 = x1 / n1 and p2 = x2 / n2. Plugging in the given values, we have:

CI = (30/65 - 47/76) ± 1.96 * sqrt(30/65 * 35/65 / 65 + 47/76 * 29/76 / 76)

CI = (0.299, 0.624)

So, the 95% confidence interval for the difference between population proportions is (0.299, 0.624), which is closest to option D