What is a p-value?

• A. The probability that the null hypothesis is true given the data.
• B. The threshold for significance.
• C. The probability of making a Type I error.
• D. The probability of observing data at least as extreme as the observed, assuming the null hypothesis is true.

Answer: (D)

The p-value measures how compatible the observed data are with the null hypothesis. It is the probability of observing data at least as extreme as what was observed, assuming the null hypothesis is true. In other words, if the null is actually true, the p-value tells you how unusual your data would be.

Extremeness depends on the test: for a two-sided test, extreme means data far in either direction from the null; for a one-sided test, extreme is only in the specified direction. This value helps you decide whether the data provide convincing evidence against the null when compared to a chosen significance level.

Remember what the p-value is not: it is not the probability that the null hypothesis is true given your data, and it is not the probability of making a Type I error by itself. The significance threshold (alpha) is a separate fixed criterion. If the p-value is smaller than alpha, you reject the null under that rule; if not, you do not reject it.