Researchers conducted an experiment to determine the effectiveness of a commercial caffeinated carbohydrate–electrolyte sports drink compared with aplacebo. Sixteen highly trained cyclists each completed two trials of prolonged cycling in a warm environment, one while receiving the sports drink and another while receiving a placebo. For a given trial,one beverage treatment was administered throughout a 2-hour variable-intensity cycling bout followed by a 15-minute

performance ride. Total work (in kilojoules) performed during the final 15 minutes was used to measure performance. The beverage order for individual subjects was randomly assigned with a period of at least five days separating the trials. Assume that the researchers verified the normality of the population of total work performed for each treatment.

(a) Why do you think the sample size was small (n = 16) for this experiment?

(b) For the sports-drink treatment, the mean total work performed during the performance ride for the n = 16 riders was 218 kilojoules, with standard deviation 31 kilojoules. Construct and interpret a 95% confidence interval for the population mean total work performed.

(c) Is it possible for the population mean total work performed for the sports-drink treatment to be less than 198 kilojoules? Do you think this is likely?

(d) For the placebo treatment, the mean total work performed during the performance ride for the n = 16 riders was 178 kilojoules, with standard deviation 31 kilojoules. Construct

and interpret a 95% confidence interval for the population mean total work performed.

(e) Is it possible for the population mean total work performed for the placebo treatment to be more than 198 kilojoules? Do you think this is likely?

(f) There searchers concluded that the caffeinated carbohydrate–electrolyte sports drink substantially enhanced physical performance during prolonged exercise compared with the placebo. Do your findings in parts (b) and (d) support the researchers’ conclusion? Explain.