97 Do nice guys finish first or last? Refer to the Nature

(March 20, 2008) study of the use of punishment in cooperation games, Exercise 18 . Recall that simple linear regression was used to model a player’s average payoff ( y ) as a straight-line function of the number of times punishment was used ( x ) by the player.

a. If the researchers want to predict average payoff for a single player who used punishment 10 times, how should they proceed?

b. If the researchers want to estimate the mean of the average payoffs for all players who used punishment 10 times, how should they proceed?