Statistical hypotheses

Let’s review the steps for conducting a hypothesis test:

1. State the null hypothesis and the alternative hypothesis.
2. Choose a significance level.
3. Find the p-value.
4. Reject or fail to reject the null hypothesis.

The first step for any hypothesis test is to state the null and alternative hypotheses. The null and alternative hypotheses are mutually exclusive, meaning they cannot both be true at the same time.

The null hypothesis is a statement that is assumed to be true unless there is convincing evidence to the contrary. The null hypothesis typically assumes that there is no effect in the population, and that your observed data occurs by chance.

The alternative hypothesis is a statement that contradicts the null hypothesis, and is accepted as true only if there is convincing evidence for it. The alternative hypothesis typically assumes that there is an effect in the population, and that your observed data does not occur by chance.

Note: The null and alternative hypotheses are always claims about the population. That’s because the aim of hypothesis testing is to make inferences about a population based on a sample.

For example, imagine you’re a data professional working for a car dealership. The company implements a new sales training program for their employees. They ask you to evaluate the effectiveness of the program.

• Your null hypothesis (H0): the program had no effect on sales revenue.
• Your alternative hypothesis (Ha): the program increased sales revenue.

Let’s explore each hypothesis in more detail.

Null hypothesis

The null hypothesis has the following characteristics:

• In statistics, the null hypothesis is often abbreviated as H sub zero (H0).
• When written in mathematical terms, the null hypothesis always includes an equality symbol (usually =, but sometimes ≤ or ≥).
• Null hypotheses often include phrases such as “no effect,” “no difference,” “no relationship,” or “no change.”

Alternative hypothesis