Teenagers’ use of emoticons in school writing. Refer to the Pew Internet and American Life...

Teenagers’ use of emoticons in school writing. Refer to the Pew Internet and American Life Project (April 2008) survey of the writing habits of U.S. teenagers, Exercise. Recall that in a random sample of 700 teenagers, 448 admitted to using at least one informal element in school writing assignments. [Note : Emoticons, such as using the symbol “:)” to represent a smile, and abbreviations, such as writing “LOL” for “laughing out loud,” are considered informal elements.] Is there evidence to indicate that less than 65% of all U.S. teenagers have used at least one informal element in school writing assignments? Test the relevant hypotheses using α =.05.

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).

Commonly Used Values of zα/2