Diamonds. In Exercise 3.37 on page 148, we considered four different color diamonds and wondered if they were associated with differing numbers of carats. In that example, after using a log transformation on the number of carats, we discovered that there was, indeed, a significant difference. Suppose we have reason to believe that diamonds of color D and E have roughly the same number of carats and diamonds of color F and G have the same number of carats (although different from D and E). a. What hypotheses would we be interested in testing? b. How would the contrast be written in symbols?