In sports, we expect top athletes to get better over time. We expect future athletes to run faster, jump higher, throw farther. One thing has remained constant, however, the percent of free throws made by basketball players has stayed almost exactly the same for 50 years (Branch, 2009). For college basketball players, the percent is about 69%, while for players in the NBA (National Basketball Association) it is about 75%. (The percent in each group is also very similar between male and female basketball players.) In each case below, find the mean and standard deviation of the distribution of sample proportions of free throws made if we take random samples of the given size. a. Samples of 100 free throw shots in college basketball. b. Samples of 1000 free throw shots in college basketball. c. Samples of 100 free throw shots in NBA basketball. d. Samples of 1000 free throw shots in NBA basketball. e. What effect does increasing sample size have on the standard deviation of the distribution? Explain.
In sports, we expect top athletes to get better over time. We expect future athletes to run faster, jump higher, throw farther. One thing has remained constant, however, the percent of free throws made by basketball players has stayed almost exactly the same for 50 years (Branch, 2009). For college basketball players, the percent is about 69%, while for players in the NBA (National Basketball Association) it is about 75%. (The percent in each group is also very similar between male and female basketball players.) In each case below, find the mean and standard deviation of the distribution of sample proportions of free throws made if we take random samples of the given size. a. Samples of 100 free throw shots in college basketball. b. Samples of 1000 free throw shots in college basketball. c. Samples of 100 free throw shots in NBA basketball. d. Samples of 1000 free throw shots in NBA basketball. e. What effect does increasing sample size have on the standard deviation of the distribution? Explain.
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