11.41 Keeping old dogs mentally sharp In an experiment with beagles ages 7–11, the dogs attempted to learn how to find a treat under a certain black-colored block and then relearn that task with a white-colored block. The control group of dogs received standard care and diet. The diet and exercise group were given dog food fortified with vegetables and citrus pulp and vitamin E and C supplements plus extra exercise and social play. All 12 dogs in the diet and exercise group were able to solve the entire task, but only 2 of the 8 dogs in the control group could do so. (Background material from N. W. Milgram et al., Neurobiology of Aging, vol. 26, 2005, pp. 77–90.)

a. Show how to summarize the results in a contingency table.

b. Conduct all steps of Fisher’s exact test of the hypothesis that whether a dog can solve the task is independent of the treatment group. Use the two-sided alternative hypothesis. Interpret.

c. Why is it improper to conduct the chi-squared test for these data?