What is the purpose of a confidence interval for the population mean?

• A. To determine whether the sample mean equals the population mean.
• B. To measure data distribution shape.
• C. To estimate a range in which the true population mean lies with a specified level of confidence.
• D. To predict individual observations.

Answer: (C)

Think of a confidence interval as estimating the true average of the whole population based on your sample, not just describing the data you collected. You start with the sample mean as your best single guess of the population mean, but because a sample can vary, there’s uncertainty. The interval adds a margin of error around that sample mean, calculated from how spread out the data are and how much sampling variation you’d expect. The result is a range that, if you repeated the study many times, would contain the true population mean a specified proportion of the time (for example, 95% of the intervals).

This emphasizes the population parameter, not individual data points, and it’s not about describing the shape of the data distribution. It also doesn’t claim the true mean is certain to lie in this one interval for this one sample; rather, it reflects the long-run frequency with which such intervals would capture the true mean if the study were repeated many times.