It is perhaps easiest to demonstrate the ideas and methods of the one-sample t-test by working through an example. To reiterate, the one-sample t-test compares the mean score of a sample to a known value, usually the population mean (the average for the outcome of some population of interest).

Note that the formula for the one‐sample t‐test for a population mean is the same as the z‐test, except that the t‐test substitutes the sample standard deviation s for the population standard deviation σ and takes critical values from the t‐distribution instead of the z‐distribution.