Which hypothesis requires a larger sample size and stronger evidence to reject the null hypothesis?

• A. Directional hypothesis
• B. Null hypothesis
• C. Non-directional hypothesis
• D. Alternative hypothesis

Answer: (C)

When you test hypotheses, whether you use a one-tailed (directional) or two-tailed (non-directional) approach changes how much evidence you need to reject the null. A non-directional hypothesis means you’re looking for any difference in either direction, so the test uses both ends of the distribution (two tails) as the rejection region. Because the alpha level is split between the two tails, the criteria to declare significance are more stringent.

With the same sample size, a two-tailed test has less power to detect a real effect in a specific direction because the data have to be extreme in either direction to reach significance. To achieve the same statistical power as a directional test, you need a larger sample size and/or a more extreme observed effect. That’s why the non-directional hypothesis typically requires more evidence and a larger sample to reject the null than a directional one.