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A Z-test is a statistical test for which the distribution of the test statistic under the null hypothesis can be estimated by a normal distribution. Because of the central limit theorem, numerous test statistics are approximately normally distributed for large samples. For every significance level, the Z-test has only one critical value which makes it extra suitable than the Student's t-test which has different critical values for each sample size. Hence, various statistical tests can be easily performed as approximate Z-tests if the sample size is large or the population variance is known. If the population variance is unknown and the sample size is small, then Student t-test is more appropriate.
Conditions for Z - Test
For the Z-test to be applicable, some conditions must be met.
- Nuisance parameters must be known, or estimated with high accurateness. Z-tests concentrates on a single parameter, and take all other unknown parameters as fixed at their true values
- The test statistic must follow a normal distribution. In general, one appeals to the central limit theorem to validate assuming that a test statistic changes normally.