A High School Coach Uses a New Technique in Training $95 \%$

A high school coach uses a new technique in training middle distance runners. He records the times for 4 different athletes to run 800 meters before and after this training. A $95 \%$ confidence interval for the difference of the means before and after the training, $\mu _ { B } - \mu _ { A }$ , was determined to be $( 2.6,4.3 )$ .

A) We are $95 \%$ confident that a randomly selected middle distance runner at this high school will have a time for the 800 -meter run that is between $2.6$ and $4.3$ seconds shorter after the training than before the training.
B) We know that $95 \%$ of the middle distance runners shortened their times between $2.6$ and $4.3$ seconds after the training.
C) Based on this sample, with $95 \%$ confidence, the average time for the 800 -meter run for middle distance runners at this high school is between $2.6$ and $4.3$ seconds longer after the new training.
D) Based on this sample, with $95 \%$ confidence, the average time for the 800 -meter run for middle distance runners at this high school is between $2.6$ and $4.3$ seconds shorter after the new training.
E) We know that $95 \%$ of all random samples done on runners at this high school will show that the mean time difference before and after the training is between $2.6$ and $4.3$ seconds.

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