from datascience import *
import numpy as np

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

scores = Table.read_table('scores_by_section.csv')
scores

max(scores.column('Midterm'))

min(scores.column('Midterm'))

scores.group('Section')

scores.group('Section', np.average).show()

observed_average = 13.6667 

# Null hypothesis: The midterm scores for section 3 are like a 
#                  random draw of 27 students from the course

# Alternative hyp: The midterm scores for section 3 are too low
#                  to be explained well by randomness alone.

random_sample = scores.sample(27, with_replacement=False)
random_sample

np.average(random_sample.column('Midterm'))

# Simulate one value of the test statistic 
# under the hypothesis that the section is like a random sample from the class

def random_sample_midterm_avg():
    random_sample = scores.sample(27, with_replacement = False)
    return np.average(random_sample.column('Midterm'))

# Simulate 100,000 copies of the test statistic

sample_averages = make_array()

for i in np.arange(100000):
    sample_averages = np.append(sample_averages, random_sample_midterm_avg())    

# Compare the simulated distribution of the statistic
# and the actual observed statistic
averages_tbl = Table().with_column('Random Sample Average', sample_averages)
averages_tbl.hist(bins = 20)
plots.scatter(observed_average, -0.01, color='red', s=120);

# (1) Calculate the p-value: simulation area beyond observed value
np.count_nonzero(sample_averages <= observed_average) / 100000
# (2) See if this is less than 5%

five_percent_point = averages_tbl.sort(0).column(0).item(round(len(sample_averages) * 0.05))
five_percent_point

# (2) See if this value is greater than observed value
observed_average

averages_tbl.hist(bins = 20)
plots.plot([five_percent_point, five_percent_point], [0, 0.35], color='gold', lw=2)
plots.title('Area to the left of the gold line: 5%');
plots.scatter(observed_average, -0.01, color='red', s=120);