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.

Example: Comparing the fraction defectives from 2 production lines.

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.

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.

Matched pair test is used to compare the means before and after something is done to the samples. A t-test is often used because the samples are often small. However, a z-test is used when the samples are large. The variable is the difference between the before and after measurements.

Example: The average weight of subjects before and after following a diet for 6 weeks