Confidence intervals around the population mean can be calculated using which principle?

Confidence intervals around the population mean are fundamentally grounded in the central limit theorem. This theorem states that as the sample size increases, the distribution of the sample mean will approach a normal distribution, regardless of the original distribution of the data being sampled. This property allows statisticians to make inferences about the population mean using sample data.

When constructing a confidence interval, the central limit theorem provides the reassurance that the variability of the sample mean can be accurately approximated, which, in turn, enables the estimation of the range within which we expect the true population mean to fall. The formula for the confidence interval incorporates the sample mean, standard deviation, and the z or t value derived from the normal distribution, all of which hinge on the validity provided by the central limit theorem.

Understanding this principle is crucial because it justifies the methods applied in estimating population parameters based on sample statistics.