Researchers were interested in whether chocolate milk might be an equivalent or even better recovery drink for athletes So they took six cyclists and had them do a strenuous interval workout Then they were allowed a four hour recovery period where three were randomly assigned to drink chocolate milk and the others were randomly assigned to drink a carb replacement drink After the recovery period, they were asked to bike until exhaustion, and their time to exhaustion (in minutes) was measured The exhaustion times for the 3 chocolate milk drinkers were 56 4, 38 5, 28 9, and for the 3 carb replacement drinkers were 21 7, 27 0, 19 6 20 possible ways of splitting the 6 observed values into group 1 and group 2 Find the value of the two sample Kolmogorov Smirnov statistic D Perform a permutation test using the K S statistic Find the value of the exact p value Perform a permutation test using the difference in medians Find the value of the exact p value Perform a permutation test using the difference in means Find the value of the test statistic and the exact p value Compare the p values Does your conclusion depend on the choice of test statistic Sample 11 Sample 12 Sample 13 Sample21 Sample22 Sample 23 19 6 21 7 27 28 9 38 5 56 4 19 6 21 7 28 9 27 38 5 56 4 19 6 21 7 38 5 27 28 9 56 4 19 6 21 7 56 4 27 28 9 38 5 19 6 27 28 9 21 7 38 5 56 4 19 6 27 38 5 21 7 28 9 56 4 19 6 27 56 4 21 7 28 9 38 5 19 6 28 9 38 5 21 7 27 56 4 19 6 28 9 56 4 21 7 27 38 5 19 6 38 5 56 4 21 7 27 28 9 21 7 27 28 9 19 6 38 5 56 4 21 7 27 38 5 19 6 28 9 56 4 21 7 27 56 4 19 6 28 9 38 5 21 7 28 9 38 5 19 6 27 56 4 21 7 28 9 56 4 19 6 27 38 5 21 7 38 5 56 4 19 6 27 28 9 27 28 9 38 5 19 6 21 7 56 4 27 28 9 56 4 19 6 21 7 38 5 27 38 5 56 4 19 6 21 7 28 9 28 9 38 5 56 4 19 6 21 7 27 Sample 11 Sample 12 Sample 13 Sample21 Sample22 Sample 23 19 6 21 7 27 28 9 38 5 56 4 19 6 21 7 28 9 27 38 5 56 4 19 6 21 7 38 5 27 28 9 56 4 19 6 21 7 56 4 27 28 9 38 5 19 6 27 28 9 21 7 38 5 56 4 19 6 27 38 5 21 7 28 9 56 4 19 6 27 56 4 21 7 28 9 38 5 19 6 28 9 38 5 21 7 27 56 4 19 6 28 9 56 4 21 7 27 38 5 19 6 38 5 56 4 21 7 27 28 9 21 7 27 28 9 19 6 38 5 56 4 21 7 27 38 5 19 6 28 9 56 4 21 7 27 56 4 19 6 28 9 38 5 21 7 28 9 38 5 19 6 27 56 4 21 7 28 9 56 4 19 6 27 38 5 21 7 38 5 56 4 19 6 27 28 9 27 28 9 38 5 19 6 21 7 56 4 27 28 9 56 4 19 6 21 7 38 5 27 38 5 56 4 19 6 21 7 28 9 28 9 38 5 56 4 19 6 21 7 27

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Researchers were interested in whether chocolate milk might be an equivalent or even better recovery drink for athletes. So they took six cyclists and had

Researchers were interested in whether chocolate milk might be an equivalent or even better recovery drink for athletes. So they took six cyclists and had them do a strenuous interval workout. Then they were allowed a four-hour recovery period where three were randomly assigned to drink chocolate milk and the others were randomly assigned to drink a carb-replacement drink. After the recovery period, they were asked to bike until exhaustion, and their time to exhaustion (in minutes) was measured. The exhaustion times for the 3 chocolate milk drinkers were 56.4, 38.5, 28.9, and for the 3 carb-replacement drinkers were 21.7, 27.0, 19.6.

20 possible ways of splitting the 6 observed values into group 1 and group 2

Find the value of the two-sample Kolmogorov-Smirnov statistic D.
Perform a permutation test using the K-S statistic. Find the value of the exact p-value.
Perform a permutation test using the difference in medians. Find the value of the exact p-value.
Perform a permutation test using the difference in means. Find the value of the test statistic and the exact p-value.
Compare the p-values. Does your conclusion depend on the choice of test statistic?

Sample 11 Sample 12 Sample 13 Sample21 Sample22 Sample 23 19.6 21.7 27 28.9 38.5 56.4 19.6 21.7 28.9 27 38.5 56.4 19.6 21.7 38.5 27 28.9 56.4 19.6 21.7 56.4 27 28.9 38.5 19.6 27 28.9 21.7 38.5 56.4 19.6 27 38.5 21.7 28.9 56.4 19.6 27 56.4 21.7 28.9 38.5 19.6 28.9 38.5 21.7 27 56.4 19.6 28.9 56.4 21.7 27 38.5 19.6 38.5 56.4 21.7 27 28.9 21.7 27 28.9 19.6 38.5 56.4 21.7 27 38.5 19.6 28.9 56.4 21.7 27 56.4 19.6 28.9 38.5 21.7 28.9 38.5 19.6 27 56.4 21.7 28.9 56.4 19.6 27 38.5 21.7 38.5 56.4 19.6 27 28.9 27 28.9 38.5 19.6 21.7 56.4 27 28.9 56.4 19.6 21.7 38.5 27 38.5 56.4 19.6 21.7 28.9 28.9 38.5 56.4 19.6 21.7 27 Sample 11 Sample 12 Sample 13 Sample21 Sample22 Sample 23 19.6 21.7 27 28.9 38.5 56.4 19.6 21.7 28.9 27 38.5 56.4 19.6 21.7 38.5 27 28.9 56.4 19.6 21.7 56.4 27 28.9 38.5 19.6 27 28.9 21.7 38.5 56.4 19.6 27 38.5 21.7 28.9 56.4 19.6 27 56.4 21.7 28.9 38.5 19.6 28.9 38.5 21.7 27 56.4 19.6 28.9 56.4 21.7 27 38.5 19.6 38.5 56.4 21.7 27 28.9 21.7 27 28.9 19.6 38.5 56.4 21.7 27 38.5 19.6 28.9 56.4 21.7 27 56.4 19.6 28.9 38.5 21.7 28.9 38.5 19.6 27 56.4 21.7 28.9 56.4 19.6 27 38.5 21.7 38.5 56.4 19.6 27 28.9 27 28.9 38.5 19.6 21.7 56.4 27 28.9 56.4 19.6 21.7 38.5 27 38.5 56.4 19.6 21.7 28.9 28.9 38.5 56.4 19.6 21.7 27