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A two-tailed $$t$$-test evaluates whether a sample mean differs from a hypothetical population mean in either direction (greater than or less than). In this test, the extreme $$5\%$$ of the distribution is split into two critical regions of $$2.5\%$$ each, one at the positive end and one at the negative end of the $$t$$ distribution.

Two-Tailed $$t$$-Test

How does a two-tailed $$t$$-test distribute the extreme $$5\%$$ of the distribution?

If a researcher conducts a two-tailed $$t$$-test to determine if a sample mean differs from a population mean, the entire extreme $$5\%$$ of the distribution is placed in a single critical region at one end of the $$t$$ distribution.

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