Studies have shown that certain ants in a colony are assigned foraging duties, which require them to
Question:
Studies have shown that certain ants in a colony are assigned foraging duties, which require them to come and go from the colony on a regular basis. Furthermore, if y is the colony size and x is the number of ants that forage, the relationship between y and x has the form y = axb, where a and b vary from species to species. Once the parameter values have been estimated for a particular kind of ant, biologists can count the (relatively small) number of ants that forage and then use the regression equation to estimate the (much larger) number of ants living in the colony. The table on p. 554 gives the results of a “calibration” study done on the red wood ant (Formica polyctena): Listed are the actual colony sizes, y, and the foraging sizes, x, recorded for fifteen of their colonies (94).
(a) Find a and b using the sums below.
(b) If the number of red wood ants seen foraging is 2500, what would be a reasonable estimate for the size of the colony from which they came?
Foraging Size, x Colony Size, y
45……………………………… 280
74……………………………… 222
118…………………………….. 288
70……………………………… 601
220…………………………….. 1,205
823…………………………….. 2,769
647…………………………….. 2,828
446…………………………….. 3,229
765…………………………….. 3,762
338…………………………….. 7,551
611…………………………….. 8,834
4,119…………………………… 12,584
850…………………………….. 12,605
11,600………………………….. 34,661
64,512………………………….. 139,043
Step by Step Answer:
Introduction To Mathematical Statistics And Its Applications
ISBN: 9780321693945
5th Edition
Authors: Richard J. Larsen, Morris L. Marx