Tests for the central location parameter of a distribution

Tests for the location parameter of a distribution and their properties and assumptions.

Test Purpose
Z Test if the mean is equal to a hypothesized value when the population standard deviation is known.
Student's t Test if the mean is equal to a hypothesized value.

Assumes the population is normally distributed. Due to the central limit theorem, the test may still be useful when this assumption is not true if the sample size is moderate. However, the Wilcoxon test may be more powerful in this situation.

Wilcoxon Test if the mean/median is equal to a hypothesized value.

Assumes the population distribution is symmetric. The mean, median, and pseudo-median are equivalent when the distribution is symmetric. Therefore, the hypotheses can be stated in terms of any of these parameters.

Sign Test if the median is equal to a hypothesized value.

Has few assumptions, but lacks power compared to the Wilcoxon and Student's t test.