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Chapter 13: Problem 30

A mother is interested in predicting the adult height of her 6 -year-old daughter. She has information on the heights of mothers and daughters in her community. Should she use a prediction interval or a confidence interval for her prediction? Explain.

Short Answer

Expert verified
The mother should use a prediction interval for her prediction since she is trying to predict a single future observation, not a population parameter.

Step by step solution

01

Understand Prediction Interval and Confidence Interval

A prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. On the other hand, a confidence interval is an estimate of an interval in which the population parameter will fall, with a certain level of confidence, based on a sample of data.
02

Relation of the Intervals to the Problem

The mother is trying to predict her daughter's future height, this is a prediction about a single observation not about a population parameter. Therefore, a prediction interval would be more suitable in this context.
03

Explain Why Prediction Interval is Suitable

Prediction intervals provide a range in which a future observation will fall with a certain probability, given the present observations. In contrast, confidence intervals estimate a range in which a population parameter will fall, given the sample data. Since the mother is attempting to estimate her daughter's future height based on the present observations of heights in her community, using a prediction interval will provide her the best estimate.

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