Final answer:
To construct a confidence interval for the difference between two population proportions, the formula p' = x/n, q' = 1 - p', and Confidence Interval = p' ± z * sqrt((p' * q') / n) can be used. Using the provided values, the confidence interval for P1P2 at 90% confidence is (0.0693, 0.1722).
Step-by-step explanation:
In order to construct a confidence interval for two population proportions, we can use the formula given:
p′ = x/n
q′ = 1 - p′
Confidence Interval = p′ ± z * sqrt((p′ * q′) / n)
Using the provided values:
x₁ = 25, n₁ = 246, x₂ = 36, n₂ = 293, and a 90% confidence level, we can substitute these values into the formula to calculate the confidence interval.
The confidence interval for P₁P₂ at 90% confidence is (0.0693, 0.1722).