Tropical flowers Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds.

Researchers believe that over time, the lengths of the flowers and the forms of the hummingbirds’ beaks have evolved to match each other. Here are data on the lengths in millimeters for random samples of two color varieties of the same species of flower on the island of Dominica:29 H. caribaea red 41.90 42.01 41.93 43.09 41.17 41.69 39.78 40.57 39.63 42.18 40.66 37.87 39.16 37.40 38.20 38.07 38.10 37.97 38.79 38.23 38.87 37.78 38.01 H. caribaea yellow 36.78 37.02 36.52 36.11 36.03 35.45 38.13 37.10 35.17 36.82 36.66 35.68 36.03 34.57 34.63

(a) A Fathom dotplot of the data is shown below. Write a few sentences comparing the distributions.

(b) Construct and interpret a 95% confidence interval for the difference in the mean lengths of these two varieties of flowers.

(c) Does the interval support the researchers’ belief that the two flower varieties have different average lengths? Explain.