I'm trying to design a system that does some binary classification. The cost of a false negative is high, so I want to ensure that I've tested thoroughly enough to minimize this chance. I would like the system to have a false negative rate of less than 1% with 95% certainty. If I expect the true positive rate to be small (around 2%), how should I calculate the required population size to reach this level of confidence? Is the one-sided test procedure the right equation to use here?

$$ N \geq \left ( \frac{z_{1-\alpha} \sqrt{p_0(1-p_0)} + z_{1-\beta} \sqrt{p_1(1-p_1)}}{p_1-p_0} \right ) ^2 $$

I'm trying to design a system that does some binary classification. The cost of a false negative is high, so I want to ensure that I've tested thoroughly enough to minimize this chance. I would like the system to have a false negative rate of less than 1% with 95% certainty. If I expect the true positive rate to be small (around 2%), how should I calculate the required population size to reach this level of confidence? Is the one-sided test procedure the right equation to use here?

$$ N \geq \left ( \frac{z_{1-\alpha} \sqrt{p_0(1-p_0)} + z_{1-\beta} \sqrt{p_1(1-p_1)}}{p_1-p_0} \right ) ^2 $$