At the point when testing a theory concerning the estimation of a populace mean, either a t-test or a z-test could be conducted. A t-test is a theory test that uses a t-fact, which takes after a t-dissemination. A z-test is a theory that uses a z-fact, which takes after a z-dissemination (a standard typical distribution).
The test should be used if the population variance is unknown and either of the following conditions holds:
The sample size is large (in general, n ≥ 30); or
The sample size is small (n ≤ 30), but the population is normally distributed or approximately normally distributed.
The z-test should be used if the population variance is normally distributed with knownvariance.
For a z-test concerning a single population mean (μ), the test statistic to be used is the z-statistic with n degrees of freedom.