The following material is derived from Florida State College at Jacksonville Library and Learning Commons ^{[1]} and is used under a Creative Commons Attribution 4.0 International Licence.

## What is Hypothesis Testing?

A **statistical hypothesis** is an assumption about a population parameter. This assumption may or may not be true. **Hypothesis testing** refers to the formal procedures used by statisticians to reject or not reject statistical hypotheses.

## Statistical Hypotheses

The best way to determine whether a statistical hypothesis is true would be to examine the entire population. Since that is often impractical, researchers typically examine a random sample from the population. If sample data are not consistent with the statistical hypothesis, the hypothesis is rejected.

There are two types of statistical hypotheses.

**Null hypothesis**. The null hypothesis, denoted by H_{0}, is usually the hypothesis that sample observations result purely from chance.**Alternative hypothesis**. The alternative hypothesis, denoted by H_{1}or H_{a}, is the hypothesis that sample observations are influenced by some non-random cause.

## Steps in Hypothesis Tests

Statisticians follow a formal process to determine whether to reject a null hypothesis, based on sample data. This process, called **hypothesis testing**, consists of four steps.

**Step 1: State the hypotheses.** This involves stating the null and alternative hypotheses. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false.

Example:

Null Hypothesis (H_{0}): There is no association between gender and brand preferences

Alternative Hypothesis (H_{1}): There is an association between gender and brand preferences

**Step 2: State the alpha value** **and the decision rule**

For example: the alpha value is usually set at 0.05;

Example: if the p-value is less than 0.05, then reject H_{0}

**Step 3: Choose the appropriate statistical test**

Examples: Chi-square, Correlation, One-sample t-test, Independent samples t-test, ANOVA

**Step 4: Interpret results. Discuss implications for managers**

- Florida State College at Jacksonville 2022, STA 2023: Statistics: basics of hypothesis testing, viewed 3 May 2022, <https://guides.fscj.edu/Statistics/hypothesis>. ↵