母集団サイズが100000のときサンプル数400で信頼度95%で誤差±5%以内の支持率が得られることの確認

result.txt

$ python test.py
population mean: 0.500000
rate of between ±5%: 0.962000

test.py

# -*- coding: utf-8 -*-

import numpy as np

N = 100000
n = 400
p = 0.5
num_trial = 10000

S = np.r_[np.ones(N * p), np.zeros(N * (1-p))]
print "population mean: %f" % np.mean(S)

results = []
for i in xrange(num_trial):
    X = np.random.choice(S, 400)
    results.append(np.mean(X))
results = np.array(results)
is_included = np.logical_and(p-0.05 <= results, results <= p+0.05)
print "rate of between ±5%%: %f" % np.mean(is_included)