Which interval will be wider when comparing a confidence interval and a prediction interval?

The prediction interval is wider than the confidence interval due to the different purposes they serve and the additional variability they account for.

A confidence interval estimates the range within which we expect the sample mean to lie based on a certain level of confidence. It primarily reflects the uncertainty associated with estimating the population mean from a sample. Therefore, the width of a confidence interval is determined by the standard error of the mean, which decreases as the sample size increases.

On the other hand, a prediction interval estimates the range in which we expect a future individual observation to fall, given a specific level of confidence. This interval takes into account not just the variability of the sample mean, but also the variability of individual data points around that mean. Since individual observations tend to vary more than the mean of a sample, prediction intervals must be broader to accommodate that extra uncertainty.

As a result, the prediction interval will generally be wider than the confidence interval, reflecting the additional uncertainty inherent in predicting individual outcomes rather than making an estimate about the population mean.