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3. (16 marks) A basketball championship tournament is held each year. The following table are the results of matches between Team A and Team B. 67 Match Score of Team A Score of Team B Home Team 1 30 27 Team A 2 73 62 Team A 3 76 78 Team B 4 51 43 Team B 5 44 40 Team A 6 Team A 7 69 54 Team B 8 60 63 Team A 9 68 Team A 70 62 Team A 11 50 54 Team B 12 86 Team A 13 56 50 Team A 14 77 68 Team B 15 64 68 Team B 16 81 75 Team A 17 70 70 Team A 55 10 65 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 1 - score B). (a) Do we have sufficient evidence to support the claim that, on average, Team A wins 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)