# MVPstats — Proportion Tests One Sample

The One-sample Binomial Test test is used to test if the sample was drawn from a population with a proportion equal to some hypothesized value. Both exact and approximate tests may be performed.

## Hypotheses

The following hypotheses may be tested:

Where is the true population proportion from which the sample was drawn, and is the hypothesized population value.

## Assumptions

1. The sample has been randomly drawn from the population (Critical)
2. The population may be modeled with a binomial distribution, which has these attributes:
1. Only two possible outcomes or classifications occur with each item examined (Critical)
2. The probability of occurrence of each classification remains fixed from item to item over time (Critical)
3. The probability of occurrence of each item sampled is independent of all other items sampled (Critical)

## Test Statistics

### Approximate Test

Where the +/- sign is determined as follows for the above hypothesis:

## Output

### Note

The p-value is flagged with an asterisk (*) when p <= alpha.