The following data refer to a random sample of prize money earned by male and female skiers racing in the 2014/2015 FIS world cup season (in Swiss Franc).
Males: 89000, 179000, 8820, 12000, 10750, 66000, 6700, 3300, 74000, 56800
Females: 73000, 95000, 32400, 4000, 2000, 57100, 4500
Enter the observations (separated by spaces) into the Permutation Test web app. Let male skiers be Group 1 and female skiers be Group 2 and let the test statistic be the difference in sample means. Is there evidence that male skiers earn more, on average, than female skiers?
a. What are the observed group means and their difference? (The subtitle of the dot plot shows this information.)
b. Why would we prefer to run a permutation test over a t test?
c. Press the Generate Random Permutation(s) button once to generate one permutation of the original data. What are the two group means and their difference under this permutation?
d. Did this one permutation lead to a difference that is less extreme or more extreme than the observed difference?
e. Click Generate Random Permutation(s) nine more times, for a total of 10 permutations. How many of them resulted in a test statistic at least as extreme as the observed one?
f. Select to generate 10,000 random permutations. How many of them resulted in a test statistic as or more extreme?
g. Find and interpret the permutation P-value.
h. Select the option to generate all possible permutations. Do you notice a big difference in the histogram and P-value based on 10,000 randomly sampled permutations and on all possible permutations?