Final answer:
The correct interpretations of a p-value of 0.02522 include strong evidence against the null hypothesis and that under the null model, a result as extreme as the one observed would be expected approximately 2.522% of the time in repeated sampling. The p-value does not measure the probability that the null hypothesis is true or that the null model fits well.
Step-by-step explanation:
Elly calculated a p-value of 0.02522. The correct interpretations of this p-value from the provided options are:
- (b) A p-value of 0.02522 means we have strong evidence against the null hypothesis.
- (c) Under the null model, we would expect a sample mean of 17 or more approximately 2.522% of the time in repeated sampling.
Option (a) is incorrect because a low p-value is an evidence against the null hypothesis, not for it. Option (d) misinterprets the p-value as the probability that the null model is a good fit, which is incorrect; the p-value is the probability of observing a result at least as extreme as the one observed, given that the null hypothesis is true.
Understanding p-values is crucial in hypothesis testing. A small p-value indicates that the observed result is unlikely under the assumption that the null hypothesis is true, which often leads to rejecting the null hypothesis in favor of the alternative. Commonly, a p-value less than 0.05 is considered significant evidence against the null hypothesis, prompting rejection.