Test for one mean


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.


The program calculates:

  • The 95% confidence interval for the mean.
  • T-value, degrees of freedom and associated P-value.

f the P-value is less than 0.05, the hypothesis that the mean is equal to the given value is rejected, and the alternative hypothesis that there is a significant difference between the two values can be accepted.

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).


  • Bland M (2000) An introduction to medical statistics, 3rd ed. Oxford: Oxford University Press.
  • Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.


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