# One-Sample Mean Test

The One-sample Mean test is used to test if the sample was drawn from a population with a mean equal to some hypothesized value. Two forms of the test are provided: when the standard deviation is known, and when it is unknown.

## Hypotheses

The following hypotheses may be tested:

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

## Assumptions

- The sample has been randomly drawn from the population (Critical)
- The population from which the sample has been drawn is normally distributed (Not Critical)
- The standard deviation is known, or unknown (Critical for small samples sizes)
- The measurements are at least Interval Level (Critical)

## Test Statistics

### Standard Deviation Known

### Standard Deviation Unknown

Where t has n -1 df

## Output

### Note

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