Difference between Z-test, F-test, and T-test

Z-Test:

A z-test is used for testing the mean of a population versus a standard, or comparing the means of two populations, with large (n ≥ 30) samples whether you know the population standard deviation or not. It is also used for testing the proportion of some characteristic versus a standard proportion, or comparing the proportions of two populations.

Example:Comparing the average engineering salaries of men versus women.

T-Test:

A t-test is used for testing the mean of one population against a standard or comparing the means of two populations if you do not know the populations’ standard deviation and when you have a limited sample (n < 30). If you know the populations’ standard deviation, you may use a z-test.

Example:Measuring the average diameter of shafts from a certain machine when you have a small sample.

F-Test:

An F-test is used to compare 2 populations’ variances. The samples can be any size. It is the basis of ANOVA.

Example: Comparing the variability of bolt diameters from two machines.