https://stats.stackexchange.com/questions/95187/is-a-p-value-a-sample-statistic-or-a-population-parameter-or-neither#comment419843_95188

comment419843_95188.py

# Ugly one-liner from an interactive session... sorry!
import numpy as np;
from scipy.stats import ttest_1samp as t;
import matplotlib.pyplot as plt;
[
  plt.scatter(
    np.arange(1,101), 
    [t(np.random.normal(size=n+1), 1).pvalue for n in range(100)],
    alpha=1/np.sqrt(100), 
    color='g')
  for j in range(1000)];

plt.show()

Output:

Looks like some sort of convergent behaviour to me.