Final answer:
The p-value is indeed the probability that the observed statistic would occur by chance if the null hypothesis were true, and small p-values provide strong evidence against the null hypothesis.
Step-by-step explanation:
The p-value is often misunderstood, so it's important to clarify what it actually represents. The statement provided is True: the p-value is the exact probability that the statistic we calculated on our observed sample could actually occur in our null distribution by chance alone. More precisely, it quantifies how likely it is to obtain a sample statistic as extreme as the one observed, or more so, assuming that the null hypothesis is true.
When the p-value is very small, this implies that the observed test statistic is very improbable under the assumption that the null hypothesis is correct. This serves as strong evidence against the null hypothesis, suggesting it should be rejected in favor of the alternative hypothesis. For instance, a p-value of less than 0.05, or 5 percent, is commonly considered as a threshold for statistical significance.