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.