### 9.2: Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.

The null hypothesis, denoted by H_{0} is a statement of no difference between the variables—they are not related. This can often be considered the status quo. As a result if you cannot accept the null, it requires some action.

The alternative hypothesis, denoted by H_{1} or H_{a}, is a claim about the population that is contradictory to H_{0} and what we conclude when we reject H_{0}. This is usually what the researcher is trying to prove.

Since the null and alternative hypotheses are contradictory, one must examine evidence to determine whether e to reject the null hypothesis or not. The evidence used is in the form of sample data.

After deciding which hypothesis the sample data supports, a decision can be made. There are two options for a decision. They are "reject H_{0}" if the sample information favors the alternative hypothesis or "do not reject H_{0}" or "decline to reject H_{0}" if the sample information is insufficient to reject the null hypothesis.

*This text is adapted from **Openstax, Introductory Statistics, Section 9.1 Null and Alternative Hypothesis*