In an experiment described by the article, a group of 15 volunteers were primed to feel powerful and then asked to roll two 10-sided dice (each having sides 0-9) and combine the results to form a number between 01 and 100 (letting 00 = 100). After rolling the dice in a secluded area, the subjects were asked to report the number they rolled. This number would determine the number of tickets they would receive for a raffle at the end of the study. The mean of their rolls was 70, much higher than the expected value of 50.5. Does this provide convincing evidence that the subjects were lying or is it plausible that they obtained a mean this high just by random chance?
(a) Design and carry out a simulation to estimate the probability that the mean value for 15 honest subjects would be at least 70, assuming that the subjects were told to roll the dice one at a time and use the first roll for the tens digit and the second roll for the ones digit.
(b) Suppose that the subjects were not told which die to use for the tens digit and which die to use for the ones digit. Design and carry out a simulation to estimate the probability that the mean value for 15 honest subjects would be at least 70, assuming that the larger die roll would be used for the tens dig