16.29 Cats versus dogs and choosing the right statistical test: The American Veterinary Association (AVA) published data on dog and cat ownership in the United States (Duff, 2017). For each example, state the variables, identify what type of variable each is, indicate which is the independent variable and which is the dependent variable, and note the appropriate statistical test. Explain why you suggested that test.

a. The data set enabled researchers to determine which are “cat states” and which are “dog states.” Specifically, for each state, the AVA provided numbers of U.S. cat-owning households and numbers of U.S. dog-owning households. Each state, therefore, had a score for number of cat households and a score for number of dog households. Some states, such as Maine and Massachusetts, have far more cat households than dog households. Other states, such as Arkansas and Alabama, show the opposite pattern. We might ask whether, overall, states tend to have more dog households or more cat households.

b. One commenter, @ninja, responded to the data from part (a): “Great data set! I wonder if there is any [relation] between urbanization and cat ownership (versus dog ownership).” Imagine that you had data for every state for both population density and number of households with cats. How could you answer @ninja’s question?

c. Another commenter, @spagolish, also responded to the data from part (a): “You can’t just ignore that the mean number of cats per household trends higher than the mean number of dogs per household. While there may be fewer cat lovers those with cats appear to have a greater need for more of them.” How could you respond to @spagolish’s comment?