06 Margin of error 1

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<iframe width="700" height="400" src="https://www.youtube.com/embed/OwPSuHXmiPw/" frameborder="0" allowfullscreen></iframe>

import numpy as np
import pandas as pd
from pandas import Series, DataFrame
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats, special

khanacademy

x = np.array(57 * [0] + 43 * [1])

sns.distplot(x)

/opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

<AxesSubplot:ylabel='Density'>

xbar = x.mean()
s = x.std(ddof=1)

mu_xbar = xbar
sigma_xbar = s/np.sqrt(len(x))

stats.norm.interval(0.95, loc=mu_xbar, scale=sigma_xbar)

(0.3324781010372837, 0.5275218989627163)

(mu_xbar - 2 * sigma_xbar, mu_xbar + 2 * sigma_xbar)

(0.3304860296087514, 0.5295139703912486)