15 points) To determine if chocolate milk is as effective as other carbohydrate replacement drinks, six male cyclists performed an intense workout followed by a drink and rest period. At the end of the rest period, each cyclist performed an endurance trial in which he exercised until exhausted, and the time until exhaustion was recorded. Each cyclist performed the entire routine on two different days. One day the drink provided was provided with chocolate milk and the other day the drink was a carbohydrate replacement. Times until exhaustion (minutes) with each drink for each cyclist are in the table below. Cyclist 1 2 3 4 5 6 Chocolate Milk 25 50 38 26 37 35 Carbohydrate Replacement 16 33 37 18 23 29 (a) (2 points) Define the parameter of interest in this situation. Use proper statistical notation. (b) (3 points) Find the sample mean difference and sample standard deviation of the differences in en- durance with the two drinks. Show all work. (c) (4 points) Find a 95% confidence interval for the parameter you defined in part (a). Round both end- points of your final confidence interval to two decimal places. (d) (3 points) Using the interval in part (b), write a sentence or two about the mean difference in time until exhaustion for the population of male cyclists drinking chocolate milk compared to the carbohydrate replacemement. (e) (2 points) From the confidence interval can we conclude that the average time until exhaustion differs between the two drinks? Why or why not? (f) (1 point) Explain one thing that the researchers could have done to obtain a narrower interval than the one you found in part (b)