Free statistical calculators

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:

$$ t = \frac {sample\ mean\ -\ hypothesized\ mean} {standard\ error\ of\ sample\ mean } $$

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

$$ t = \frac {\bar{x} - k} { s / \sqrt{n} } $$

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.
• Kirkwood BR, Sterne JAC (2003) Essential medical statistics, 2^nd ed. Oxford: Blackwell Science.

How to cite this page

• MedCalc Software Ltd. Test for one mean calculator. https://www.medcalc.org/calc/test_one_mean.php (Version 23.2.6; accessed June 15, 2025)

See also

• MedCalc manual: Test for one mean