Final answer:
A confidence interval (CI) provides an estimate range that likely contains the true population parameter. The confidence level represents the probability that this interval does actually contain the true value if the study was repeated multiple times.
Step-by-step explanation:
The likelihood that an identified precision interval, known as a confidence interval (CI), contains the true (but unknown) population value refers to the confidence level associated with the interval estimate. When we say a CI has a certain confidence level, like 95 percent, we mean that if we were to take repeated samples and compute a CI for each sample, we would expect that 95 percent of the constructed intervals would contain the true population parameter.
Alpha (α) is a term closely related to the confidence level, representing the probability that the CI does not contain the unknown population parameter. For instance, a 90 percent confidence level corresponds to alpha (α) being 0.10, indicating a 10 percent chance that the CI does not include the true value. To attain a higher confidence level, one often needs a larger interval, which means accepting more variability in the CI estimate, especially when dealing with smaller sample sizes. Conversely, larger sample sizes, which reduce variability, can allow for a smaller interval while maintaining confidence in encompassing the true population parameter.