Null hypothesis

Definition

The null hypothesis is a statement that there is no effect or no difference, and it serves as the default or starting assumption in hypothesis testing. It is denoted as $H_0$ and is tested against the alternative hypothesis.

5 Must Know Facts For Your Next Test

1. The null hypothesis ($H_0$) usually includes an equality (e.g., $\mu = \mu_0$).
2. Rejecting the null hypothesis suggests that there is significant evidence for the alternative hypothesis.
3. Failing to reject the null hypothesis means there isn't enough evidence to support the alternative hypothesis, not that $H_0$ is true.
4. The significance level ($\alpha$) determines the threshold for rejecting the null hypothesis.
5. Common significance levels are 0.05, 0.01, and 0.10.

Review Questions

• What symbol is typically used to represent the null hypothesis?
• What does it mean if you fail to reject the null hypothesis?
• How is a significance level ($\alpha$) related to the rejection of a null hypothesis?

Related terms

Alternative Hypothesis:

A statement that contradicts the null hypothesis, suggesting there is an effect or a difference. It is denoted as $H_a$ or $H_1$.

Significance Level:

The probability of rejecting the null hypothesis when it is actually true, commonly denoted as $\alpha$. Typical values are 0.05, 0.01, and 0.10.

$p$-Value: $p$-Value measures the strength of evidence against the null hypothesis. A lower $p$-value indicates stronger evidence against $H_0$.