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Milestone
(adapted by Dan Teague from the COMAP curricular project ARISE.)

Two varieties of a tiny biting insect called a midge were discovered in the jungles of Brazil by biologists W.L. Grogan and W.W. Wirth. One kind is the deadly Apf midge that is the carrier of a debilitating disease which causes swelling in the brain if a human is bitten by the infected midge. The other form is the Af midge that is quite harmless and a valuable pollinator. In an efort to distinguish the two types, the biologist took many measurements of the midges that they caught. Two measurements for some of the randomly selected insects are recorded in the table.

 Wing span (cm) 1.78 1.86 1.96 2 2 1.96 Antenna Length (cm) 1.14 1.2 1.3 1.26 1.28 1.18

Af Midges (harmless)

 Wing span (cm) 1.72 1.64 1.74 1.7 1.82 1.82 1.9 1.82 2.08 Antella Length(cm) 1.24 1.38 1.36 1.4 1.38 1.48 1.38 1.53 1.56

1) Is it possible to distinguish between Apf and Af midges on the basis of wing and antenna length? Determine a method of distinguishing the two varieties of midges. Plot the data and then use the data to determine an appropriate model to describe the relationship between Wing Span and Antenna Length.

2) If you make an error in your classification, would you rather call an Af midge Apf or an Apf midge Af? Which error is worse? Why? How does this affect your classification scheme?

3) There seem to be more Af midges than Apf midges, so if a midge is captured, it is more likely to be an Af midge. How could this be taken into account?

4) It is important to know if a midge is dangerous or not. Suppose that biologists capture five more midges. Their measures were:

 A B C D E Wing Span (cm) 1.70 2.02 1.88 1.96 1.78 Antenna Length (cm) 1.36 1.32 1.30 1.54 1.22

How would you classify them? Which midges do you have the most confidence that you have classified correctly?