02 Examples identifying conditions for inference on two proportions#

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

Examples identifying conditions for inference on two proportions fig 1Examples identifying conditions for inference on two proportions fig 2

\[\begin{split}\begin{array}{ll} (1)&\mbox{SRS}\\ (2)&\mbox{Independence}:\ \#\ \mbox{Sample} \le 10\%\ *\ \#\ \mbox{Population}\\ (3)&\mbox{Normality}:\ n\hat{p}\ge 10, n(1-\hat{p})\ge 10\\ \\ (1)&\mbox{SRS}:\ \mbox{Both samples are SRS}\\ (2)&\mbox{Independence}:\ \#\ \mbox{Sample}_i \le 10\%\ *\ \#\ \mbox{Population}_i\ \mbox{for both $i=1,2$}\\ (3)&\mbox{Normality}:\ n_i\hat{p}_i\ge 10, n_i(1-\hat{p}_i)\ge 10\ \mbox{for both $i=1,2$}\\ \end{array}\end{split}\]