Reconsider the baseball data from Example 7.2 (FirstBase). Suppose for now that the data had been from 44 different players rather than paired data on the same 22 players. Test whether one of the methods is significantly different than the other.
a. Perform a simulation of a randomization test to compare the two groups (assuming that the data had been from 44 different players). Report the p-value. What conclusion would you reach?
b. How do the p-value and conclusion change from this analysis, as compared to the paired analysis conducted in Example 7.2?
c. Explain how this exercise demonstrates the value of having conducted a matched pairs experiment to investigate the question of whether one method of running the bases is better than the other method.