Final answer:
The given statement is true as the p-value indeed represents the likelihood of observing a sample mean that is as extreme or more extreme than the sample mean derived, under the assumption that the null hypothesis is true. It's used to determine the statistical significance of the test results. Option A is the correct answer.
Step-by-step explanation:
The question asks whether it's true or false that under the assumption that the null hypothesis is true as an equality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample. The answer to this is A. True.
The p-value is a fundamental concept in hypothesis testing within statistics, a branch of mathematics. It represents the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. A p-value is calculated depending on the type of test being performed (left, right, or two-tailed) and is usually evaluated against a significance threshold (α), commonly set at 0.05 or 5%.
If the p-value is smaller than the significance level, it suggests that the observed sample mean (or sample statistic) is unlikely to have occurred by chance if the null hypothesis were true, leading to the rejection of the null hypothesis. In contrast, when the p-value is larger than the significance level, there isn't enough evidence to reject the null hypothesis. So, the p-value helps analysts to make an informed decision about the null hypothesis, utilizing statistical evidence.