Under what condition can a null hypothesis be rejected?

• A. When there is no evidence
• B. When there is enough evidence to doubt its truth
• C. Whenever p-value is high
• D. When the sample size is small

Answer: (B)

Rejecting a null hypothesis happens when the data provide convincing evidence that the assumed parameter value under that hypothesis is unlikely. In practice this is expressed by a p-value below the pre-set significance level (often 0.05), meaning the observed data would be quite improbable if the null were true. Saying there is enough evidence to doubt its truth captures this idea: the data push us to question the validity of the null value. If there is no strong evidence against it, or the p-value is large, we do not reject the null. A small sample size can make detecting a real effect harder (lower power), but the decision to reject is driven by the strength of the evidence, not size alone.