Sockeye salmon swim sometimes hundreds of miles from the Pacific Ocean, where they grow up, to rivers for spawning. Kokanee are a type of freshwater sockeye that spends their entire lives in lakes before swimming to rivers to mate. In both types of fish, the males are bright red during mating. This red coloration is caused by carotenoid pigments, which the fish cannot synthesize but get from their food. The ocean environment is much richer in carotenoids than the lake environment, which raises the question: how do kokanee males become as red as the sockeye? One hypothesis is that the kokanee is much more efficient than the sockeye at using available carotenoids. This hypothesis was tested by an experiment in which both sockeye and kokanee individuals were raised in the lab with low levels of carotenoids in their diets (Craig and Foote 2001). Their skin color was measured electronically (as a* units on an L*a*b* standard that correlates strongly with redness). The data are as follows and are plotted in the accompanying histograms:

a. List two methods that would be appropriate to test whether there was a difference in mean skin color between the two groups.

b. Use a transformation to test whether there is a difference in mean between these two groups. Is there a difference in the mean of kokanee and sockeye skin color?

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Kokanee: 1.11.1.11, 1.34,1.34, 1.55,1.55, 1.53,1.53, 1.50,1.50, 1.71,1.71, 1.87,1.87, 1.86,1.86, 1.82,1.82, 2.01,2.01, 1.95,1.95, 2.01,2.01, 1.66. 1.66, 1.49,1.49, 1.59,1.59, 1.69,1.69, 1.80,1.80, 2.00,2.00, 2.30.2.30. Sockeye: 0.98,0.98, 0.88,0.88, 0.97,0.97, 0.99,0.99, 1.02,1.02, 1.03,1.03, 0.99,0.99, 0.97,0.97, 0.98,0.98, 1.03,1.03, 1.08,1.08, 1.15.1.15, 0.90, 0.90, 0.95,0.95, 0.94,0.94, 0.99.0.99.