The NHST model is a statistic, such as a t-test, for determining whether a given variable causes the effect being tested. NHST tests often make certain assumptions. The NHST model (z-test and t-test) makes assumptions regarding the distribution of the tested variable.
One such assumption relates to the normal distribution of data. Z-statistic and t-test assume that the data is normally distributed as long as the sampling is done independently and the sample is large enough. The sample mean (X-bar), computed using the CLM method, is also assumed to be equivalent to the population mean (μ). Z-test also assumes that the researcher knows the standard deviation (σ). T-test does not have this assumption.