A study of injuries to in-line skaters used data from the National Electronic Injury Surveillance System, which collects data from a random sample of hospital emergency rooms. The researchers interviewed 160 people who came to emergency rooms with injuries from in-line skating. Wrist injuries (mostly fractures) were the most common.

(a) The interviews found that 53 people were wearing wrist guards and 7 of these had wrist injuries. Of the 107 who did not wear wrist guards, 49 had wrist injuries. Why should we not use the large-sample confidence interval for these data? One count is only 7, and the guidelines for using the large-sample method call for all counts to be at least 25. The counts are only 7 and 49, and the guidelines for using the large-sample method call for all counts to be at least 100. The counts are only 7 and 49, and the guidelines for using the large-sample method call for all counts to be at least 50. One count is only 7, and the guidelines for using the large-sample method call for all counts to be at least 10.

(b) The plus four method adds one success and one failure in each sample. What are the sample sizes and counts of successes after you do this? Population Sample size Number of successes wrist guards no wrist guards

(c) Give the plus four 95% confidence interval for the difference between the two population proportions of wrist injuries. (Use pguards − pno guards. Round your answers to four decimal places.)