# 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

• Each trial is independent of the other
• The number of “n” trials is fixed
• The probability of success, “p”, is the same for each trial

## Sampling distribution of the proportion

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).

## Estimating standard error and confidence intervals of the proportion

Approximate standard error