A key statistic used by football $ coaches to evaluate players is a players 40-yard sprint time.

Question:

A key statistic used by football $ coaches to evaluate players is a player€™s 40-yard sprint time. Can a drill be developed for improving a player€™s speed in the sprint? Researchers at Northern Kentucky University designed and tested a speed-training program for junior varsity and varsity high school football players. The training program included 50-yard sprints run at varying speeds, high knee running sprints, butt kick sprints, €œcrazy legs€ straddle runs, quick feet drills, jumping, power skipping, and all-out sprinting. 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 and saved in the SPRINT file. 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.