.Help me to solve the following questions.

Topic 2: Hypothesis Testing (Single Sample & Single Population) The U.S. military awards the 'purple heart' award to all service members who are injured in the course of duty. Recently it was discovered that many soldiers who received concussions in the course of serving in Afghanistan and Iraq have not received purple hearts. (http://www.npr.org/2010/09/09/129606127/purple hearts-elusive-for-traumatic- brain-injuries.) The military wants to know how widespread this neglect is. In particular they want to know if fewer than 50 percent of soldiers with concussions have been awarded the purple heart. Unfortunately their records aren't computerized, so it would be prohibitively expensive to examine the records of every soldier who has received a concussion in the last ten years. Instead they take a random sample of fifty soldiers who were recently diagnosed with concussions received in the line of duty and find that 23 of them received purple hearts. They approach you. and ask for your help looking into this issue. A. Set up your research and null hypothesis, such that, if you reject the null hypothesis, you're asserting that fewer than 50% of all soldiers who were concussed in the line of duty received purple hearts. (2 points) B. Calculate the standard error and test statistic for this hypothesis test. (2 points) C. Calculate and interpret the p-value for this hypothesis test. (4 points)4. Consider the following two player game. Note that the dashed line indicates an information set. P1 LI R P2 P1 PI L2 R2 (a) Give an example of a pure strategy for Player 1. (b) Write down the normal-form representation of this extensive-form game. (c) Find all the pure strategy Nash equilibria of the game, if any. (d) Find all the pure strategy subgame perfect Nash equilibria, if any. Show your procedure. (e) Are there any other subgame perfect Nash equilibria? If yes, find one. If no, explain.1. (a) Let the function / : C \\ (0) - C be given by f(x tip) = ]tix x2+ 12 for x, y c R such that x + y' * 0. Determine the sets A, = (z E C : f is complex differentiable at z) and A2 = (ze C : f is analytic at z). [8 marks] (b) Consider the set S= [ze C : (z-1| > 1}n tz : Rez