Question

What's the formula for the standard error of the difference between the estimates of the population proportions, used in a confidence interval for the difference between two proportions?

Answer 1

Answer:

$s_{p_1-p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2} }$

Step-by-step explanation:

The formula for the standard error of the difference between the estimates od the population proportions is:

$s_{p_1-p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2} }$

This is expected, as the variance of a sum (or a substraction) of two random variables is equal to the sum of the variance of the two variables.

Then, the standard error (or standard deviation) is the square root of this variance.