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# Free statistical calculators

## Test for one mean calculator

## Description

The Test for one mean can be used to test the hypothesis that a sample mean is equal to a given mean (with unknown standard deviation) or certified value.

## Required input

- The observed
**sample mean**,**standard deviation**and**sample size**(n). **Test mean is equal to:**enter the value to compare the mean to.

## 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).

## How to cite this page

- MedCalc Software Ltd. Test for one mean calculator. https://www.medcalc.org/calc/test_one_mean.php (Version 22.026; accessed June 18, 2024)

## Literature

- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.
- Kirkwood BR, Sterne JAC (2003) Essential medical statistics, 2
^{nd}ed. Oxford: Blackwell Science.