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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 Joumal, 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 -.01 .1 .24 .25 .05 .28 1.25 .2 1.14 .32 .34 .3 1.09 .05 0 .04 .17 0 .21 15 3 102 .12 1.14 .1 .08 .51 .36 .1 .01 34 38 44 10.8 Based on Gray, M.,& Sauerbeck, J. A. "Speed training program for high school football players." The Sport Joumal, 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. 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.Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol 8414, 2010) study on the current trend in the design of social robots, Exercise 2.7 (p. 38). Recall that in a random sample of social robots obtained through a Web search, 28 were built with wheels. The number of wheels on each of the 28 robots is reproduced in the accompanying table. 3. Estimate #, the average number of wheels used on all social robots built with wheels, with 90% confidence. b. Practically interpret the interval, part a. c. Refer to part a. In repeated sampling. what proportion of all similarly constructed confidence intervals will contain the true mean, A? Some: Chew, 5, et al. "De sucial rubuls walk or rall!" International Conference on Social Roboties, Vol. 6414, 2010 (adapted from Figure ?). (Reference Exercise 2.7) 27 Do social robots walk or roll? According to the United Nations, social robots now outnumber industrial ro- bots worldwide. A social (or service) robot is designed to entertain, educate, and care for human users. In a paper published by the International Conference on Social Robotics (Vol. 6414, 2010), design engineers investigated the trend in the design of social robots. Using a random sample of 106 social robots obtained through a Web search, the engineers found that 63 were built with legs only, 20 with wheels only, & with both legs and wheels, and 15 with neither logs nor wheels. This information is portrayed in the accompanying graphic. a. What type of graph is used to describe the data? b. Identify the variable measured for each of the 106 robot designs. c. Use the graph to identify the social robot design that is currently used the most. d. Compute class relative frequencies for the different calegories shown in the graph. e. Use the results from part d to construct a Parcto diagram for the data. 70 63 60 50 40 Number of Robots 20 15 None Both Legs Only Wheels Only Type of Robotic Limbs