Chapter 19, Problem 32CE

Christina Sanders is a member of the women’s basketball team at Windy City College. Last season, she made 55% of her free throw attempts. In an effort to improve this statistic, she attended a summer camp devoted to shooting techniques. The next 20 days she shot 100 free throws each day. She carefully recorded the number of free throws that she made each day. The results are reported below.

To interpret, the first day she made 55 out of 100, or 55%. The second day she made 61 shots, the third day, 52 shots, the tenth day 58, the eleventh day 57 shots. The last day she made 67 out of 100, or 67%.

1. a. Develop a control chart for the proportion of shots made. Over the 20 days of practice, what percent of attempts did she make? What are the upper and lower control limits for the proportion of shots made?
2. b. Is there any trend in her proportion made? Does she seem to be improving, staying the same, or getting worse?
3. c. Find the percent of attempts made for the last 5 days of practice. Use the hypothesis testing procedure, formula (15-1), to determine if there is an improvement from 55%.