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.

-.01 .1 .1 .24 .25 .05 .28 .25 .2 .14

.32 .34 .3 .09 .05 0 .04 .17 0 .21

.15 .3 .02 .12 .14 .1 .08 .5 .36 .1

.01 .9 .34 .38 .44 .08 0 0 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 2).

a. Find a 95% confidence interval for the true mean decrease LO6 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.