A cautionary simulation about selecting on the outcome.

For each of trials repetitions:

• draw n values from $\mathcal{N}(0, 1)$, so the null hypothesis $\mu = 0$ is true
• compute the sample mean, then discard every value below it
• run a one-sided z-test on what is left, testing $\mu > 0$ with known $\sigma = 1$
• count it as a rejection if the p-value is below alpha

Return the fraction of repetitions that rejected. Under a correct procedure this would sit near alpha; filtering on the sample's own mean is what breaks it.

Seed np.random.seed(seed) inside solve, immediately before drawing.

Input

n = 20
trials = 400
alpha = 0.05
seed = 0

Output

0.815