Pooled Proportion Test Statistic

Compute the pooled two-proportion z-statistic for two groups of 0/1 outcomes under the null hypothesis that both groups have the same underlying rate.

Implement solve(a, b).

Returns. Return the z-statistic as a Python float, positive when a has the higher rate. If every outcome in both groups is identical the pooled variance is zero and the statistic is not finite.

Examples

Example 1

Input:

solve([1, 1, 0, 1, 0, 0, 1, 1], [0, 0, 1, 0, 0, 1, 0, 0])

Output:

1.511858

Example 2

Input:

solve([1, 0, 1, 0], [1, 0, 1, 0])

Output:

0.0