Final answer:
A confidence interval provides an interval estimate of the population mean, and represents a range within which we can be certain to a specified confidence level that the population mean lies. It accounts for sample variability, with its width influenced by the sample size and the desired confidence level.
Step-by-step explanation:
An interval estimate of the population mean is provided by a confidence interval, which gives a range of values, constructed from sample data, that is likely to contain the population mean with a certain level of certainty, or confidence level. Unlike a point estimate, such as the sample mean which provides a single best estimate, a confidence interval accounts for the variability in the sample and provides an estimated range (e.g., between x - 0.2 and x + 0.2) where the population mean is expected to fall. The width of this interval is affected by the sample size and the desired confidence level; larger samples and lower confidence levels generally producing narrower intervals. However, if we want a higher degree of certainty, we need to accept a larger interval, as the confidence level would increase with a larger interval (f). If repeated samples were taken, about 90 percent (or another specified level) of these confidence intervals would contain the true population mean, as per the confidence level chosen.