Speed training in football. Researchers at Northern Kentucky University designed and tested a speed-training program for junior varsity and varsity high school football players (The Sport Journal, Winter 2004). Each in a sample of 38 high school athletes was timed in a 40-yard sprint prior to the start of the training program and timed again after completing the program. The decreases in times (measured in seconds) are listed in the table. [Note: A negative decrease implies that the athlete’s time after completion of the program was higher than his time prior to training.] The goal of the research is to demonstrate that the training program is effective in improving 40-yard sprint times.

a. Find a 95% confidence interval for the true mean decrease in sprint times for the population of all football players who participate in the speed-training program.

b. Based on the confidence interval, is the training program really effective in improving the mean 40-yard sprint time of high school football players? Explain.

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