A biologist is studying the life cycle of the avian schistosome that causes swimmer€™s itch. His study uses Menganser ducks for the adult parasites and aquatic snails as intermediate hosts for the larval stages. The life history is cyclic. (For more information, see swimmersitch.org/.) As a part of this study, the biologist and his students used snails from a natural population to measure the distances (in cm) that snails travel per day. The conjecture is that snails that had a patent infection would not travel as far as those without such an infection. Here are the measurements in cm that snails traveled per day. There are 39 in the infected group and 31 in the control group.
Distances for Infected Snail Group (ordered):

Distances for Control Snail Group (ordered):

(a) Find the sample means and sample standard deviations for the two groups of snails.
(b) Make box plots of the two groups of snails on the same graph.
(c) For the control snail group, test the hypothesis that the distances come from an exponential distribution. Use as an estimate of θ. Group the data into 5 or 10 classes, with equal probabilities for each class. Thus, the expected value will be either 6.2 or 3.1, respectively.
(d) For the infected snail group, test the hypothesis that the distances come from a gamma distribution with α = 2 and θ = 42. Use 10 classes with equal probabilities so that the expected value of each class is 3.9. Use Minitab or some other computer program to calculate the boundaries of the classes.

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