from datascience import *
import numpy as np

%matplotlib inline
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')

united = Table.read_table('united.csv')
united = united.with_column('Row', np.arange(united.num_rows)).move_to_start('Row')

def sample_median(size):
    return np.median(united.sample(size).column('Delay'))

# (Population) Parameter
np.median(united.column('Delay'))

# (Sample) Statistic
sample_median(10)

# (Sample) Statistic
sample_median(100)

sample_medians_10 = make_array()
sample_medians_100 = make_array()
sample_medians_1000 = make_array()

num_simulations = 2000

for i in np.arange(num_simulations):
    new_median_10 = sample_median(10)
    sample_medians_10 = np.append(sample_medians_10, new_median_10)
    new_median_100 = sample_median(100)
    sample_medians_100 = np.append(sample_medians_100, new_median_100)
    new_median_1000 = sample_median(1000)
    sample_medians_1000 = np.append(sample_medians_1000, new_median_1000)

sample_medians = Table().with_columns('Size 10', sample_medians_10, 
                                      'Size 100', sample_medians_100,
                                      'Size 1000', sample_medians_1000)

sample_medians.hist(bins = np.arange(-5, 30))

population_proportions = make_array(.26, .74)
population_proportions

sample_proportions(100, population_proportions)

def panel_proportion():
    return sample_proportions(100, population_proportions).item(0)

panel_proportion()

panels = make_array()

for i in np.arange(10000):
    new_panel = panel_proportion() * 100
    panels = np.append(panels, new_panel)

Table().with_column(
    'Number of Black Men on Panel of 100', panels
).hist(bins=np.arange(5.5,40.))

# Plotting details; ignore this code
plots.ylim(-0.002, 0.09)
plots.scatter(8, 0, color='red', s=30);

## Mendel had 929 plants, of which 709 had purple flowers
observed_purples = 709 / 929
observed_purples

predicted_proportions = make_array(.75, .25)
sample_proportions(929, predicted_proportions)

def purple_flowers():
    return sample_proportions(929, predicted_proportions).item(0) * 100

purple_flowers()

purples = make_array()

for i in np.arange(10000):
    new_purple = purple_flowers()
    purples = np.append(purples, new_purple)

Table().with_column('Percent of purple flowers in sample of 929', purples).hist()

# Plotting details; ignore this code
plots.ylim(-0.02, 0.25)
plots.scatter(observed_purples * 100, 0, color='red', s=30);

Table().with_column('Discrepancy in sample of 929 if the model is true', abs(purples- 75)).hist()

# Plotting details; ignore this code
plots.ylim(-0.02, 0.6)
plots.scatter(abs(observed_purples * 100 - 75), 0, color='red', s=30);

abs(observed_purples * 100 - 75)