# Test for one mean

## 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.

## Results

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).

## Literature

- 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.

## Link

Go to Test for one mean.