Exercise 4.62 describes a situation in which game theory students are randomly assigned to play either Game 1 or Game 2, and then are given an exam containing questions on both games. Two one-tailed tests were conducted: one testing whether students who played Game 1 did better than students who played Game 2 on the question about Game 1, and one testing whether students who played Game 2 did better than students who played Game 1 on the question about Game 2. The p-values were 0.762 and 0.549, respectively. The p-values greater than 0.5 mean that, in the sample, the students who played the opposite game did better on each question. What does this study tell us about possible effects of actually playing a game and answering a theoretical question about it? Explain.  

Exercise 4.62

Two professors at the University of Arizona were interested in whether having students actually play a game would help them analyze theoretical properties of the game. The professors performed an experiment in which students played one of two games before coming to a class where both games were discussed. Students were randomly assigned to which of the two games they played, which we’ll call Game 1 and Game 2. On a later exam, students were asked to solve problems involving both games, with Question 1 referring to Game 1 and Question 2 referring to Game 2. When comparing the performance of the two groups on the exam question related to Game 1, they suspected that the mean for students who had played Game 1 (μ₁) would be higher than the mean for the other students μ₂, so they considered the hypotheses H₀: μ₁ = μ₂ vs H_a: μ₁ > μ₂.