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Chapter 13: Problem 29

A logging company has the diameter of each of a large number of trees and wants to estimate the mean number of usable cubic feet of wood the company will get if it cuts the trees down. Working with a sample of trees, company planners find the regression line that predicts the volume of lumber (in cubic feet) on the basis of the diameter of the tree. Should they use a prediction interval or a confidence interval? Explain.

Short Answer

Expert verified
The company should use a confidence interval because they want to estimate the mean number of usable cubic feet for the entire group of trees, not the individual trees.

Step by step solution

01

Understand the difference between Prediction Interval and Confidence Interval

A prediction interval provides an interval within which the response variable likely falls for a given value of the explanatory variable. A confidence interval provides an interval within which the mean response falls for all the possible values of the explanatory variable.
02

Apply Understanding To Context

The company is trying to estimate the mean number of usable cubic feet of wood it will get when it cuts the trees down. They are not trying to predict the amount of wood for an individual tree; instead, they want to predict the mean for the entire forest.
03

Decide Which Interval to use

In this case, since they are trying to estimate the mean (an average), they should use a confidence interval. This interval is used to reflect where the true population parameter (in this case, the mean volume of lumber from the trees) is likely to lie.

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