Final answer:
Option (C), The term that describes the probability of another sample producing a mean as far or further in the tail end is the p-value. It is used to evaluate the evidence against the null hypothesis in statistical hypothesis testing.
Step-by-step explanation:
The statement 'The _____ is the probability of another sample producing a mean as far or further in the tail end' is referring to the p-value. This value is an indication of how extreme the observed result is, assuming that the null hypothesis is true. In statistical hypothesis testing, the p-value helps us determine the significance of our results in the context of a null hypothesis.
When constructing a confidence interval, the confidence level, such as 90%, tells us that if we were to take repeated samples and construct confidence intervals from these samples, approximately 90 percent of these confidence intervals would contain the true population mean. The p-value is different; it is 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 higher p-value indicates that there is stronger evidence in favor of the null hypothesis, while a lower p-value indicates stronger evidence against it. For example, at a 5 percent significance level (α = 0.05), if the p-value is less than 0.05, we would reject the null hypothesis, as there is less than a 5 percent probability of the sample mean falling as far or further in the tail end of the distribution if the null hypothesis were true. This corresponds to answer choice C, which correctly fills the blank in the original question.