Differentiate a prediction interval from a confidence interval: which statement is accurate?

Differentiate a prediction interval from a confidence interval: which statement is accurate?

• A. A confidence interval estimates the likely range for a population parameter; a prediction interval estimates the range for an individual future observation.
• B. They are the same.
• C. Confidence interval is wider than prediction interval always.
• D. Prediction interval estimates population parameter.

Answer: (A)

The main idea here is the target of each interval. A confidence interval bounds the true parameter of the population (such as the mean) using the information from your sample. A prediction interval, on the other hand, provides a range where a single new future observation is likely to fall, given the model and the data you’ve seen. This difference in purpose is what makes the statement accurate: it correctly assigns each interval to its respective target. In addition, prediction intervals incorporate more variability because they account for the natural randomness of individual observations in addition to the uncertainty about the parameter estimate, which is why they’re not asking for the population parameter itself. The other options misstate these roles: they’re not the same; a prediction interval isn’t for estimating a population parameter; and while a prediction interval is often wider than a confidence interval, that isn’t described as a universal rule in every situation.

The main idea here is the target of each interval. A confidence interval bounds the true parameter of the population (such as the mean) using the information from your sample. A prediction interval, on the other hand, provides a range where a single new future observation is likely to fall, given the model and the data you’ve seen. This difference in purpose is what makes the statement accurate: it correctly assigns each interval to its respective target.

In addition, prediction intervals incorporate more variability because they account for the natural randomness of individual observations in addition to the uncertainty about the parameter estimate, which is why they’re not asking for the population parameter itself. The other options misstate these roles: they’re not the same; a prediction interval isn’t for estimating a population parameter; and while a prediction interval is often wider than a confidence interval, that isn’t described as a universal rule in every situation.