Sample Size for Proportion

Estimate the sample size needed per group to detect a difference between two proportions $p_{1}p\_1$ and $p_{2}p\_2$ with a two-sided test, using $z_{\alpha \mathrm{/}2}=1.96z\_\{\backslash alpha/2\}=1.96$ (5% significance) and $z_{\beta }=0.84z\_\backslash beta=0.84$ (80% power).

Implement solve(p1, p2).

Returns. Return an int, rounded up. Both rates must lie in $[0,1][0,1]$ and must differ; otherwise ValueError is raised.

Examples

Example 1

Input:

solve(0.1, 0.15)

Output:

685

Example 2

Input:

solve(0.5, 0.6)

Output:

387