14. A nutritionist randomly divided 15 bicyclists into 3 groups of 5 each. The first group was given a vitamin supplement to take with each of their meals during the next 3 weeks. The second group was instructed to eat a particular type of high-fiber whole-grain cereal for the next 3 weeks. The final group was instructed to eat as they normally do. After the 3-week period elapsed, the nutritionist had each of the bicyclists ride 6 miles. The following times were recorded.

(a) Are the data consistent with the hypothesis that neither the vitamin nor the fiber cereal affected the bicyclists’ speeds? Use the 5 percent level of significance.

(b) Find confidence intervals for all quantities μi − μj that, with 95 percent confidence, are valid.

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Vitamin group: Fiber cereal group: Control group: 15.6 16.4 17.2 15.5 16.3 17.1 16.3 15.8 15.9 17.2 16.4 16.4 16.0 15.4 16.8