Test for one mean
The Test for one mean is 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.
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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, 2nd ed. Oxford: Blackwell Science.
How to cite this page
- MedCalc Software Ltd. Test for one mean. https://www.medcalc.org/en/calc/test_one_mean.php (Version 23.6.1; accessed June 14, 2026)
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