What term refers to an interval with limits at either end that specifies the probability of including the estimated parameter?

The term that refers to an interval with limits at either end, which indicates the probability of including the estimated parameter, is known as a confidence interval.

A confidence interval provides a range of values within which the true parameter (like a population mean) is expected to lie, with a certain level of confidence (commonly 95% or 99%). This means that if you were to take many samples and calculate a confidence interval from each one, a specified percentage of those intervals would contain the true population parameter. It emphasizes the degree of uncertainty around the estimation and allows researchers to understand the variability inherent in sampling.

In contrast, the other terms listed do not represent this concept. A p-value indicates the strength of the evidence against the null hypothesis but does not provide a range for parameter estimates. Standard error measures the extent to which the sample mean deviates from the population mean, while a statistical hypothesis refers to a proposed explanation that can be tested. None of these options encapsulate the idea of a range with limits that communicates an estimated parameter's reliability in the same way a confidence interval does.