Binomial distribution and binomial test

How do we analyze proportions?

Binomial distribution equation

Binomial distribution: the distribution “successes” of many independent trials. There are only two possible outcomes, success and non-success.

Assumptions

Proportion of X successes out of n trials (p-hat).

Population standard error of p-hat.

Binomial test: used to test hypothesis that the population proportion (p) is the same as the null expectation (p₀).

	# Six-sided die flipped 24 times and lands on three exactly 6 times
	binom.test(x = 6, n = 24, p = 1 / 6, alternative = "greater")

	# Flip coin 30 times and it lands on heads exactly 19 times
	binom.test(x = 19, n = 30, p = 1 / 2, alternative = "greater")

view raw binomial_test.r hosted with ❤ by GitHub

R code

	# Binomial test in Python

	from scipy.stats import binom_test

	# Six-sided die flipped 24 times and lands on three exactly 6 times
	x = binom_test(x=6, n=24, p=1/6, alternative='greater')
	print(x)

	# Flip coin 30 times and it lands on heads exactly 19 times
	y = binom_test(x=19, n=30, p=1/2, alternative='greater')
	print(y)