A hypothesis test based on approximating the probability histogram of the z statistic under the null hypothesis by the normal curve.
A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution.[dubious – discuss] Due to the central limit theorem, many test statistics are approximately normally distributed for large samples. Therefore, many statistical tests can be performed as approximate Z-tests if the sample size is large.
The most general way to obtain a Z-test is to define a numerical test statistic that can be calculated from a collection of data, such that the sampling distribution of the statistic is approximately normal under the null hypothesis. Statistics that are averages (or approximate averages) of approximately independent data values are generally well-approximated by a normal distribution. An example of a statistic that would not be well-approximated by a normal distribution would be an extreme value such as the sample maximum.