Speed training in football. Refer to The Sport Journal (Winter 2004) study on the effectiv...

Speed training in football. Refer to The Sport Journal (Winter 2004) study on the effectiveness of a speed-training program for football players, Exercise. The decreases in 40-yard sprint times (time after training minus time before training) for 38 players are saved in the SPRINT file. An athlete’s sprint performance will be classified as “Improved” if the “after” time is less than the “before” time, and classified as “Not Improved” if otherwise.

a. Find an estimate for the true proportion of all high school athletes who attain improved sprint times after participating in the speed-training program.

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b. Convert the estimate, part a, into a 95% confidence interval. Give a practical interpretation of the result.

Speed training in football. 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 Sport Journal , Winter 2004). The training program included 50-yard sprints run at varying speeds, high knee running sprints, butt kick sprints, “crazy 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. [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

Based on Gray, M.,&Sauerbeck, J. A. “Speed training program for high school football players.” The Sport Journal , Vol. 7, No. 1, Winter 2004 (Table).

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.

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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.