Final answer:
A p-value is a probability that represents the chance of observing the study results, or more extreme, by random chance if the null hypothesis is valid. A small p-value, typically less than 0.05, indicates strong evidence against the null hypothesis, which may lead to its rejection.
Step-by-step explanation:
True, a p-value is indeed a probability. It is the probability that the statistically significant result (or one more extreme) observed in a study could have occurred purely by chance, assuming the null hypothesis is true. A small p-value, typically less than 0.05, indicates strong evidence against the null hypothesis, thereby suggesting it should be rejected.
For instance, if we observe a p-value of 0.01 in an experiment, it signifies there is only a 1% probability that the results are due to random chance, which provides substantial evidence to reject the null hypothesis. It is important to compare the p-value with the established significance level (α) to determine if the results are statistically significant.
The p-value provides us with a quantitative tool for making decisions in hypothesis testing. Its interpretation can be contextualized depending on the nature of the experiment and the distribution from which the test statistic is derived, such as a normal or t-distribution.