Which statement is true regarding a small p-value?

A small p-value suggests strong evidence against the null hypothesis. In hypothesis testing, the p-value measures the probability of observing the data, or something more extreme, assuming that the null hypothesis is true. When the p-value is low, it implies that such observed data would be very unlikely under the assumption of the null hypothesis being correct. Consequently, researchers often use a threshold for the p-value, often 0.05, below which they would reject the null hypothesis, indicating strong evidence in favor of the alternative hypothesis. This leads to the conclusion that there is a significant effect or difference within the studied data.

On the other hand, larger p-values indicate that the evidence against the null hypothesis is weak, and a p-value itself does not dictate a need for larger sample sizes; rather, sample size considerations often relate to the power of a test. Additionally, while a smaller p-value can be associated with an increased likelihood of Type I errors if the null hypothesis is rejected too readily, this relationship is not a defining feature of small p-values themselves. Thus, the correct understanding hinges on recognizing that a small p-value is indicative of strong evidence against the null hypothesis.