Suppose Jimmy and Bobby are two long-time competitors on the same track team in the $400$-meter dash.
Jimmy and Bobby have ran $10$ races this year. Jimmy has averaged $56.2$ seconds with a standard deviation of $1.3$ seconds, while Bobby has averaged $55.8$ seconds with a standard deviation of $1.3$ seconds. Bobby asked the coach to perform a two-sample T-test to determine if he is significantly better than Jimmy this year.
What conclusion does the coach make?