import math, random




###############################################################################
# P-hacking
###############################################################################

# A procedure that erroneously rejects the null hypothesis only 5% 
# of the time will - by definition - 5% of the time erroneously reject 
# the null hypothesis:

def run_experiment():
    """flip a fair coin 1000 times, True = heads, False = tails"""
    return [random.random() < 0.5 for _ in range(1000)]

def reject_fair_coin(experiment):
    """using the 5% significance levels"""
    num_heads = len([flip for flip in experiment if flip])
    return num_heads < 469 or num_heads > 531

random.seed(0)

# Perform 1000 experiments (each experiment flips a coin 1000 times)
# 
experiments = [run_experiment() for _ in range(1000)]

num_rejections = len([experiment
                      for experiment in experiments
                      if reject_fair_coin(experiment)])

print(num_rejections)