Definition

In a test of hypothesis, the null hypothesis is a statement made about one or more process/population distributions, usually indicating status quo (no difference) or a baseline argument, with the aim of rejecting it.

Examples

An example of a null hypothesis is

H_{0}: There is no difference between the two process means. (µ_{1} - µ_{2} = 0)

This statement will be contrasted against the alternative hypothesis, which represents the state of the population(s) under study if the null hypothesis were false. The null and alternative hypotheses are mutually exclusive (only one or the other can be true at any given time, but never both) and together reflect all possible states for the population(s).

Other examples of null hypotheses:

H_{0}: The mean test score after a new training procedure is not higher than that before the procedure by more than 10 points.

(µ_{after} - µ_{before} ≤ 10)

This is often written as

(µ_{after} - µ_{before} = 10)

The alternative then would be:

H_{0}: The mean test score after a new training procedure is higher than that before the procedure by more than 10 points.

(µ_{after} - µ_{before} > 10)

Application

The goal of the hypothesis test is to reject or fail to reject the null by submitting the data to comparison with a decision criterion.