There are three basic types of ‘tails’ that hypothesis tests can have:

- Right-tailed test: where the alternative hypothesis includes a ‘<’ symbol.
- Left-tailed test: where the alternative hypothesis includes a ‘>’ symbol.
- Two-tailed test: where the alternative hypothesis includes a ≠.

You can also think of ‘tails’ in terms of rejection regions:

- When performing a right-tailed test, we reject the null hypothesis if the test statistics are greater than the critical value.
- When performing a left-tailed test, we reject the null hypothesis if the test statistics are less than the critical value.
- When performing a right-tailed test, we reject the null hypothesis if the test statistics are greater than or less than the critical value.

### Example

Consider a null hypothesis that states that cars traveling on a particular road have a mean velocity of 40 miles/hour:

- A
**right-tailed test**would state that cars traveling on a particular road have a mean velocity less than 40 miles/hour. - A
**left-tailed test**would state that cars traveling on a particular road have a mean velocity greater than 40 miles/hour. - A
**two-tailed test**would state that cars traveling on a particular road have a mean velocity greater than*or*less than 40 miles/hour.

## Need more?

Khan Academy has a great video that walks you through one-tailed and two-tailed hypothesis tests:

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