THE ROLLOUT CHECK
Beginner
Difficulty: Easy Tags: Probability & Statistics
Story
Robinhood A/B-tests a new order-ticket UI against the existing one. Before anyone calls the difference "real," it needs a proper two-proportion z-test, not just eyeballing two percentages.
The Math
p_hat = (x1 + x2) / (n1 + n2)
SE = sqrt( p_hat * (1 - p_hat) * (1/n1 + 1/n2) )
z = (p2 - p1) / SE
Two-sided p-value from the standard normal CDF, where p1 = x1/n1 and p2 = x2/n2 (group 1 =
control, group 2 = treatment).
Input Format
n1 x1 n2 x2
Output Format
p1 p2 z pvalue, 6 decimals.
Constraints
1 <= n1, n2 <= 10^7,0 <= x_i <= n_i- Time limit: 1.0 second.
Example
Input
5000 250 5000 300
Output
0.050000 0.060000 2.193172 0.028295
Keywords
probability-and-statistics
Python
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