Final answer:
The prediction interval is generally narrower than the confidence interval when both have the same confidence level.
Step-by-step explanation:
The prediction interval is generally narrower than the confidence interval when both have the same confidence level. Let's take an example:
Suppose we want to estimate the height of a population of students. We collect a sample and calculate a 95% confidence interval, which gives us a range of heights that we can be 95% confident in containing the true population mean height. Now, if we want to make a prediction interval for the height of an individual student, it would generally be narrower than the confidence interval. This is because the confidence interval accounts for variability in the sample mean, while the prediction interval accounts for both variability in the sample mean and variability in individual observations.
So, in summary, when comparing a prediction interval and a confidence interval with the same confidence level, the prediction interval is typically narrower.