4. (16 marks) A basketball championship tournament is held each year. The following table are the results of matches between Team A and Team B. Match Score of Team A |Score of Team B Home Team 30 27 Team A 73 62 Team A 76 78 Team B 51 43 Team B 44 40 Team A 84 67 Team A 69 54 Team B 63 Team A 55 Team A 62 Team A 54 Team B 65 Team A 50 Team A 14 77 68 Team B 15 64 68 Team B 16 81 75 Team A The victory margin of Team A in a game is defined as the difference of the score of Team A to the score of Team B (i.e., score A - score B). Assume a = 0.05 for all the following tests. (a) Do we have sufficient evidence to support the claim that, on average, Team A win by more than 3 points in a game (i.e., the mean of victory margin of Team A is greater than 3)? (8 marks) (b) Test the hypothesis that the standard deviation of the victory margin of Team A is more than 5 points. (8 marks)