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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?

A

Any inferential procedure in this context does not make sense.

B

Bobby is faster at the alpha $5\%$ level, but not at the $1\%$ level.

C

Jimmy is faster at the alpha $5\%$ level, but not at the $1\%$ level.

D

Bobby is faster at the alpha $1\%$ level.

E

There is insufficient evidence at the alpha $10\%$ level to determine who is faster.

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