A few years ago, this class considered problem 8-106 (old number was 8.94) (oxyg

Question

A few years ago, this class considered problem 8-106 (old number was 8.94) (oxygen concentration in a stream). In this problem we compute a prediction interval (where future values could be). The prediction interval in this problem is:

-1.2975<= xn+1<= 7.8275

One student was particularly perplexed and took offense with his result and sent an email saying “this prediction interval (equation 8-28, page 297) gives me a negative number for the lower interval…it makes no practical sense that [oxygen] measurements in a stream below a dam could have a negative number. The answers are obviously ridiculous.”

Evaluate and explain this situation and the student’s thinking. Is it logically possible to have negative oxygen concentrations? Is the student correct, is this result ridiculous? What is the prediction interval telling us here? Does this student understand what a prediction interval is used for?  

Explanation / Answer

a. In the answer to the given problem, the statistical answer gives a range for oxygen concentration in a stream, which is the prediction interval ranging to a negative number at a minimum. The student practically and correctly points that oxygen concentration cannot be negative.

b. Though the answer is correct statistically but needs to be adjusted for practical reasons, as it is not possible to have negative oxygen concentration in natural setting / circumstances.

c. The student is correct, as the result is completely theoretical with no practical aspect considered.

d. The prediction interval, in the above solution, points that the future oxygen concentration has a prediction interval [-1.2975, 7.8275] meanign that the Oxygen concentration can be anywhere between these two values.

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