# Free statistical calculators

## Test for one mean calculator.

## Computational notes

This procedure calculates the difference of an observed mean with a hypothesized value. A significance value (P-value) and 95% Confidence Interval (CI) of the observed mean is reported. The P-value is the probability of obtaining the observed mean in the sample if the null hypothesis value were the true value.

The P-value is calculated using the one sample *t*-test, with the value *t* calculated as:

or when the hypothesized mean is *k* and the standard deviation is *s*:

The P-value is the area of the *t* distribution with *n*−1 degrees of freedom, that falls outside ± *t* (see Values of the *t* distribution table).

## Literature

- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.