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To illustrate a two-tailed test, consider a scenario with $$24$$ degrees of freedom where the critical values for an alpha level of $$.05$$ are $$2.064$$ and $$-2.064$$ (represented by red vertical lines in the accompanying distribution). Any computed $$t$$ score falling below $$-2.064$$ (the lowest $$2.5\%$$ of the distribution) or above $$2.064$$ (the highest $$2.5\%$$ of the distribution) is considered extreme. If a sample's $$t$$ score falls into either of these outer regions, the resulting $$p$$-value is less than $$.05$$, providing sufficient statistical evidence for the researcher to reject the null hypothesis.

Example of a Two-Tailed Test

In a two-tailed test with an alpha level of .05 and critical values of -2.064 and 2.064, what conclusion is drawn if a sample's computed t score falls below -2.064 or above 2.064?

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