Answer:
[tex]s_{p_1-p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2} }[/tex]
Step-by-step explanation:
The formula for the standard error of the difference between the estimates od the population proportions is:
[tex]s_{p_1-p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2} }[/tex]
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.
