Suppose we believe that with probability p a person will play a certain Nash equilibrium, and that this probability is the same for all people

 Suppose we believe that with probability p a person will play a certain Nash equilibrium, and that this probability is the same for all people. We do not know p, but have reason to believe it is about 25%. To test this hypothesis against the two-tailed alternative, we put 100 subjects through an experiment and observe 20 of them playing the Nash strategy. Based on the experimental results, conduct a parametric test, test whether p = 25% when a (type 1 error) = 0.05. 2. Problem 2 The mean weight of items coming from a production line is 83 pounds. On average, 19 out of 20 of these individual weights are between 81 and 85 pounds. The average weights of six randomly selected items are plotted. What proportion of these points will fall between the limits 82 and 84 pounds? What is the precise nature of the random sampling hypothesis that you need to adopt to answer this question? Consider how it might be violated and what the effect of such a violation might be on your answer. 3. Problem 3 Fifteen judges rated two randomly allocated brands of beer, A and B, according to taste (scale: 1 to 10) as follows: