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Chapter 13: Problem 28

A dean of students at a college wishes to estimate the typical future cumulative GPA for all first-year students who earned a \(2.0\) GPA during their first year. Should she use a prediction interval or a confidence interval? Why?

Short Answer

Expert verified
The dean should use a confidence interval if she wishes to estimate the average GPA for all first-year students who earned a 2.0 GPA during their first year. If she wishes to predict specific future individual GPAs, she should use a prediction interval.

Step by step solution

01

Understanding Confidence Interval

A confidence interval in statistics is a range of values that are likely to contain a population parameter. It provides 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. In this case, if the dean uses a confidence interval, she would be estimating the average future cumulative GPA for all first-year students who earn a 2.0 GPA in their first year.
02

Understanding Prediction Interval

A prediction interval in contrast to a confidence interval, is an estimate of an interval in which future observations will fall, with a certain probability, given what has already been observed. The prediction interval is wider than the confidence interval because it accommodates more uncertainty. It includes the error in the estimate of the mean plus the randomness in any individual value. If the dean uses a prediction interval, she would be estimating individual future cumulative GPAs for students who earn a 2.0 GPA in their first year.
03

Deciding Between Confidence Interval and Prediction Interval

If the dean wants to estimate a range in which the typical (average) future GPA would fall for the entire group of students who earned a 2.0 GPA in their first year, she should use a confidence interval. This would give the expected average GPA. However, if she wants to estimate what individual GPAs might be in the future, she should use a prediction interval.

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