A two-tailed test is an approach to hypothesis testing where researchers reject the null hypothesis if their calculated test statistic falls into the extreme regions of either the positive or negative tail of the distribution. This method utilizes two distinct critical values—an upper bound and a lower bound—and is appropriately chosen when researchers expect the sample mean to differ from the hypothetical population mean, but lack strong theoretical justification to predict whether it will be higher or lower.

Two-Tailed Test

In statistical hypothesis testing, what is the primary function of a critical value?

A critical value is a predetermined threshold on a statistical distribution used to make a decision about the null hypothesis. Derived from the specified alpha level (such as $$\alpha = 0.05$$) and the degrees of freedom, it marks the boundary of the most extreme expected scores. If a calculated test statistic falls beyond this critical value, the result is deemed statistically significant, leading to the rejection of the null hypothesis.

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When conducting a one-sample $$t$$-test, the degrees of freedom ($$df$$) are calculated by subtracting one from the total sample size ($$N - 1$$). This specific calculation dictates the exact shape of the $$t$$ distribution, enabling researchers to accurately identify the $$p$$ value associated with their test statistic.

Degrees of Freedom (One-Sample t-Test)

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