sampling + Regression to mean + Confidence Intercals (b)

import numpy as np
import random
import matplotlib.pyplot as plt
import scipy.stats

def create_pop(n):
    # to randomly create population distribution set with given population size.
    # replication of uniform distribution
    distrib = 1000 * np.random.random_sample((n, ))
    return distrib

def graph_distribution(dist, name):
    plt.hist(dist)
    plt.title(name)
    plt.show()

def sample_procedure(dist):
    sample_size = int(raw_input("Enter the sample size:"))
    sample_repeats = int(raw_input("Enter the number of times to repeat the experiment:"))
    sample_means = []
    # some essential data
    standard_deviation_population = np.std(population)
    mean_population = np.mean(population)
    standard_error = standard_deviation_population / (sample_size)**0.5
    #confidence interval = µ +/- Z.95*SE
    confidence_interval = scipy.stats.norm.interval(.95, mean_population, standard_error)
    lower = confidence_interval[0]
    upper = confidence_interval[1]
    count = 0
    for _ in range(sample_repeats):
        # create sample distribution set with given sample size, and calculate the sample mean
        # repeat the process for given times by while loop
        sample = np.random.choice(dist, (sample_size, ))
        this_mean = np.mean(sample)
        sample_means.append(this_mean)
        #keep track of the number of times the population mean falls within the confidence intervals
        if lower <mean_population < upper:
            count += 1
    print "Here's what the sample mean distribution looks like."

    plt.hist(sample_means)
    plt.title('Sample Means')
    plt.show()

    print "The mean of the sample means is:", np.mean(sample_means)
    print "The Standard Error / The standard deviation of the sample means is:", np.std(sample_means)
    print ""

#####################################

print "First create a (pseudo)-random distribution."
population_size = int(raw_input("Enter a population size:"))
print "..."
population = create_pop(population_size)
print "Here's what the population distribution looks like."
graph_distribution(population, 'Population Distribution')

print "The population mean is:", np.mean(population)
print ""
print "The population standard deviation is:", np.std(population)
print ""
print "For the second step, enter the size of the samples to draw --with replacement-- from the population distribution, and how many times to repeat this procedure in order to create a distribution of sample means."

sample_flag = True

while sample_flag:
    sample_procedure(population)
    #track the number of times the population mean falls within the confidence intervals
    # and get the proportion from the sample_repeats base
    #I expect to get the probability close to 0.95(confidence interval)
    probability = float(count) /sample_repeat
    print probablilty
    print "Perform sampling procedure again? Note that if no, then the population distribution will be lost."
    decision = raw_input("Type y or n:")
    if decision == 'n':
        sample_flag = False
    else:
        print "Doing procedure again."