Refer to the Nature (March 20, 2008) study of the use of punishment in cooperation games, Exercise 11.18. Recall that college students repeatedly played a version of the game "prisoner's dilemma," and the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player.
a. A test of no correlation between cooperation use (x) and average payoff (y) yielded a p-value of .33. Interpret this result.
b. A test of no correlation between defection use (x) and average payoff (y) yielded a p-value of .66. Interpret this result.
c. A test of no correlation between punishment use (x) and average payoff (y) yielded a p-value of .001. Interpret this result.