Final answer:
The statement about the p-value being the probability of obtaining a sample statistic as extreme as the one observed, assuming the null hypothesis is true, is correct. A p-value less than 0.05 often leads to rejection of the null hypothesis, supporting the alternative hypothesis. The interpretation of the p-value varies with the specific test and hypothesis being considered.
Step-by-step explanation:
In a hypothesis test, the statement 'the p-value is the probability of obtaining a sample statistic at least as extreme as the value actually obtained when we assume that the null hypothesis is true' is indeed true. The p-value represents how likely it is to observe a test statistic as extreme as the sample statistic, under the assumption that the null hypothesis is correct. When this value is very small, it indicates that such an extreme observed outcome is very unlikely if the null hypothesis were true. This is why a small p-value, typically less than 0.05 or even 0.01, provides strong evidence against the null hypothesis, leading analysts to reject it in favor of the alternative hypothesis.
The interpretation of the p-value depends on the context of the problem. For example, if the null hypothesis posits that a population proportion is 0.25, and a p-value of 0.0103 is obtained from the data, this implies that there is only a 1.03% probability of observing a sample proportion of 0.4048 or more extreme, under the null hypothesis. Such a low p-value is usually considered strong evidence to reject the null hypothesis.