What does a p-value represent in hypothesis testing?

• A. The probability of observing the data, or more extreme, if the null hypothesis is true
• B. The probability that the null hypothesis is true
• C. The probability that the alternative hypothesis is true
• D. The effect size of the observed result

Answer: (A)

In hypothesis testing, a p-value measures how compatible your observed data are with the assumption that the null hypothesis is true. It is the probability, under that null assumption, of obtaining results as extreme as what you actually saw (or more extreme). It does not tell you the probability that the null hypothesis is true, nor the probability that the alternative is true. It also doesn’t indicate the size of the effect—it can be small if you have a large sample even for a tiny effect. For example, if you test whether a coin is fair and observe 60 heads out of 100 flips, the p-value reflects how likely such a result is under p = 0.5; a small p-value suggests the observed result is unlikely under the null, leading you to consider rejecting it at your chosen significance level.