An entomologist was interested in determining if Colorado potato beetles were ­randomly distributed over a potato field or if they tended to appear in clusters. The field was gridded into evenly spaced squares, and counts of the beetle were conducted. The following data give the number of squares in which various numbers of beetles were observed. If the appearance of the potato beetle is random, a Poisson model should provide a good fit to the data.

a. The average number of beetles per square is 0.5. Does the Poisson distribution provide a good fit to the data?
b. Based on your results in part (a), do Colorado potato beetles appear randomly across the field?

Transcribed Image Text:

Number of Beetles 0 3 45 or more Total 1.011 Number of squares 678 227 56 28 8 14