What is the difference between a 95% confidence interval and a 95% prediction interval?

What is the difference between a 95% confidence interval and a 95% prediction interval?

• A. Both intervals estimate the same quantity.
• B. A 95% confidence interval estimates the population parameter with unknown true value, while a 95% prediction interval estimates where a new individual observation will fall.
• C. Confidence interval is for a future observation; Prediction interval estimates the parameter.
• D. Prediction interval gives the exact true parameter value.

Answer: (B)

The key idea is that these two intervals answer different questions about uncertainty. A 95% confidence interval is about the true population parameter (for example, the mean). It reflects how uncertain we are about that parameter given the data, and if we repeated the study many times, about 95% of the intervals we'd compute would contain the true parameter. A 95% prediction interval, in contrast, is about where a single new observation from the population will fall. It incorporates both the uncertainty in our estimate of the parameter and the natural variability of individual observations around that parameter. Because it accounts for this extra source of variability, the prediction interval is typically wider than the confidence interval. So the best way to describe the distinction is: the confidence interval estimates the unknown population parameter; the prediction interval estimates the range where a new future observation is likely to fall. The other statements mix up which interval targets which quantity and misunderstand what a prediction interval represents.

The key idea is that these two intervals answer different questions about uncertainty. A 95% confidence interval is about the true population parameter (for example, the mean). It reflects how uncertain we are about that parameter given the data, and if we repeated the study many times, about 95% of the intervals we'd compute would contain the true parameter.

A 95% prediction interval, in contrast, is about where a single new observation from the population will fall. It incorporates both the uncertainty in our estimate of the parameter and the natural variability of individual observations around that parameter. Because it accounts for this extra source of variability, the prediction interval is typically wider than the confidence interval.

So the best way to describe the distinction is: the confidence interval estimates the unknown population parameter; the prediction interval estimates the range where a new future observation is likely to fall. The other statements mix up which interval targets which quantity and misunderstand what a prediction interval represents.