Maximum likelihood
Location tests are the most familiar "Z"-tests. Another class of "Z"-tests arises in maximum likelihood estimation of the parameters in a parametric statistical model. Maximum likelihood estimates are approximately normal under certain conditions, and their asymptotic variance can be calculated in terms of the Fisher information. The maximum likelihood estimate divided by its standard error can be used as a test statistic for the null hypothesis that the population value of the parameter equals zero. More generally, if formula_8 is the maximum likelihood estimate of a parameter θ, and θ0 is the value of θ under the null hypothesis,