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Chapter 13: Problem 34

Explain the difference between a confidence interval and a prediction interval. How can a prediction level of \(95 \%\) be interpreted?

Short Answer

Expert verified
A confidence interval estimates a population parameter such as the mean, while a prediction interval predicts future individual observations. A 95% prediction level interprets that 95 out of 100 times, the future observation will fall within the predicted interval.

Step by step solution

01

Define Confidence Interval

A confidence interval is a range of values, derived from a statistical model, that is likely to contain the value of an unknown parameter. It's an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.
02

Define Prediction Interval

A prediction interval is an estimate of an interval in which a future observation will fall, with a certain confidence level, given the observations that were already observed. Both the confidence level and prediction level describe the uncertainty of these intervals.
03

Difference between Confidence Interval and Prediction Interval

The main difference between a confidence interval and a prediction interval is what they deal with. A confidence interval deals with population parameters like the mean, whilst a prediction interval deals with future individual observations. In other words, confidence intervals are used to predict a population parameter, whereas prediction intervals predict an individual value.
04

Interpretation of 95% Prediction Level

A prediction level of 95% means that 95 out of 100 times, the predicted interval will contain the future observation. In other words, we can be 95% confident that the future observation will fall within the predicted interval.

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Most popular questions from this chapter

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