What's the Difference Between a One-Tailed and Two-Tailed Test?

A one-tailed test looks for a change in one specified direction, while a two-tailed test looks for a change in either direction. The wording of the claim determines the test through the alternative hypothesis.

How the Tail Is Chosen

Suppose a company claims that the mean battery life is 10 hours.

The null hypothesis contains equality, so all three tests use $H_0:\mu=10$. You must choose the direction before examining the sample results; choosing it afterwards would bias the test.

For example, if the sample mean is above 10 but the preselected alternative is $H_1:\mu<10$, the result does not support that alternative. You may not switch to an upper-tailed test after seeing the data.

At significance level $\alpha=0.05$, a one-tailed test places the full rejection probability in one tail. A two-tailed test divides it between both tails, placing $\alpha/2=0.025$ in each tail. Consequently, a one-tailed test has more power to detect an effect in its specified direction, but it cannot test for an effect in the opposite direction.

For a GDC-generated p-value, compare it directly with $\alpha$:

• If $p<\alpha$, reject $H_0$.
• If $p\geq\alpha$, there is insufficient evidence to reject $H_0$.

A common misconception is that the sign of the sample result decides whether the test is one- or two-tailed. It does not: the research question and $H_1$ decide this before calculations begin.

IB Exam Technique

This is SL 4.11 hypothesis testing and may appear on either GDC-active paper. State $H_0$ and $H_1$, use the correct one- or two-tailed GDC test, compare $p$ explicitly with $\alpha$, and conclude in context. Never write “accept ”; write “insufficient evidence to reject .”