A Z-test is commonly used in statistics to determine whether a given hypothesis is true in a normal distribution or bell curve. Z-tests are optimal for sample sizes of 30 or greater, while student t-tests are best used for lower sample sizes.
Z-tests may also work for data sets that do not follow a normal distribution. In all Z-tests, the nuisance parameters must be known or estimated within a high level of certainty. The first step in running a Z-test is to state the null hypothesis and an alternate hypothesis. The Z-test statistic then can be calculated after choosing an alpha level and finding Z's value within the Z table.