guys.
I want to make an hypothesis test about two proportions $p_{1},p_{2}$ and the condition is that $p_1 \geq kp_2$, in particular $p_1 \geq 2p_2$. So I made this hypothesis $$H_0:p_1 \geq 2p_2; H_1:p_1 \lt 2p_2 $$
I've seen examples of hypothesis tests using difference of proportions and using a Z test, but I don't know if it is correct. I have something like $(\hat{p_1}-\hat{p_2})-(p_1 - p_2)$, but I don't know what to do because $p_1 - p_2 = p_2$. I also have calculated proportions $\hat{p_1},\hat{p_2}$ and a significance $\alpha$. How can I use this info to calculate a Z score?