Why Confidence Interval is always wider than Prediction interval?

Question

I was given a problem asking that and I'm not quite sure how to answer it. If anyone can please explain me

Since it seems to be a homework, please add `[self-study]` tag and check http://stats.stackexchange.com/tags/self-study/info — Tim, Nov 15 '16 at 14:23
Prediction intervals are actually always wider than confidence intervals. A detailed explantion is given here: https://stats.stackexchange.com/a/271232/180467 — Igor Franzoni Okuyama, Nov 27 '19 at 13:08

score 7 · Answer 1 · answered Nov 15 '16 at 14:21

Is it?

I have seen someone compute a confidence interval for the mean, and use it as if it was a prediction interval for a future observation. The trouble is, confidence intervals for the mean are much narrower than prediction intervals, and so this gave him an exaggerated and false sense of the accuracy of his forecasts. Instead of the interval containing 95% of the probability space for the future observation, it contained only about 20%.

(source http://robjhyndman.com/hyndsight/intervals/)

Also: https://www.graphpad.com/support/faqid/1506/ – Ashe Nov 15 '16 at 14:25 — Ashe, Nov 15 '16 at 14:25

score 5 · Answer 2 · answered Nov 15 '16 at 19:24

5

I can be very, very confident what the average age of a United States citizen is if I've taken enough samples. But if you pick a person at random, I basically have no idea how old they are. One has almost nothing to do with the other.

answered Nov 15 '16 at 19:24

David Schwartz

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Variance of sample mean vs variance of population. Is this what the op was asking? – innisfree Nov 15 '16 at 22:43
@innisfree That's pretty much what it comes down to. – Dave Nov 27 '19 at 14:24

Why Confidence Interval is always wider than Prediction interval?

2 Answers2