African swine fever virus is a disease of wild boars that is spread in part by contact between living pigs and the carcasses of dead pigs. As part of an investigation into the patterns of contact between living and dead pigs, researchers placed cameras near pig carcasses in the woods near Greifswald, Germany (Probst et al. 2017). Over 1136 nights of observation in total, they detected groups of wild pigs on 298 nights. The number of nights during which various numbers of groups of pigs visited are given in the following table:

a. What probability distribution would describe the number of pig groups detected on nights of the study if pig groups visited randomly in time and independently of one another?

b. Using the frequency data given, test whether the number of pig group visits conforms to the probability distribution in (a).

c. Do the data best support the conclusion that the number of pig groups per night are clumped, random, or dispersed in time?

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Number of wild pig groups 00 11 22 33 44 55 66 77 88 99 >9> 9 Frequency of nights 838838 191191 5959 3737 00 88 22 00 00 11 00