One-Sample Mean Test

The One-sample Mean test is used to test if the sample was drawn from a population with a mean equal to some hypothesized value. Two forms of the test are provided: when the standard deviation is known, and when it is unknown.


The following hypotheses may be tested:

TF - 1sample Means Hyp

Where Mu is the true population mean from which the sample was drawn, and Mu0 is the hypothesized population value.


  1. The sample has been randomly drawn from the population (Critical)
  2. The population from which the sample has been drawn is normally distributed (Not Critical)
  3. The standard deviation is known, or unknown (Critical for small samples sizes)
  4. The measurements are at least Interval Level (Critical)

Test Statistics

Standard Deviation Known

One-Sample Means z-test

Standard Deviation Unknown

One-Sample Means t-test

Where t has n -1 df


TF OneSample means Test Output


The p-value is flagged with an asterisk (*) when p <= alpha.