# Two Tailed Test: Definition, Examples

Hypothesis Testing > Two Tailed Test

## What is a Two Tailed Test?

A two tailed test tells you that you’re finding the area in the middle of a distribution. In other words, your rejection region (the place where you would reject the null hypothesis) is in both tails.

For example, let’s say you were running a z test with an alpha level of 5% (0.05). In a one tailed test, the entire 5% would be in a single tail. But with a two tailed test, that 5% is split between the two tails, giving you 2.5% (0.025) in each tail.

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## Two Tailed T Test

You may want to compare a sample mean to a given value of x with a t test. Let’s say your null hypothesis is that the mean is equal to 10 (μ = 10). A two tailed t test will test:

• Is the mean greater than 10?
• Is the mean less than 10?

If you choose an alpha level of 5%, and the f statistic is in the top 2.5% or bottom 2.5% of the probability distribution, then there is a significant difference in the means. That situation will also result in a p-value of less than 0.05. A small p-value gives you a reason to reject the null hypothesis.