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37 - To decide which interval to use you must answer this...

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To decide which interval to use, you must answer this question: do you want to predict the mean BAC for all students who drink 5 beers, or do you want to predict the BAC of one individual student who drinks 5 beers? Both of these predictions may be interesting, but they are two different problems. The actual prediction is the same, ŷ = 0.077. But the margin of error is different for the two kinds of prediction. Individual students who drink 5 beers don’t all have the same BAC. So we need a larger margin of error to pin down Steve’s result than to estimate the mean BAC for all students who have 5 beers. To estimate the mean response, we use a confidence interval. It is an ordinary confidence interval for the mean response when x has the value x*, which is μy = α + β x*. This is a parameter, a fixed number whose value we don’t know. To estimate an individual response y, we use a prediction interval. A prediction interval estimates a single random response y rather than a parameter like μy. The response y is not a fixed number.
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