A study performed in a Boston area high school showed a link between drinking soda and weak bones. Among 57 active children who do not drink soda, 5 suffered fractures. Among 107 active children who reported drinking soda, 38 suffered fractures. The study did not specify how much soda the children drank. (The Denver Post, 6/15/2000, "New study links cola, weak bones.")
a. Using a two-sample test of proportions, determine whether this study provides significant evidence at the 1% level to suggest that the probability of getting a fracture is lower for kids that do not drink soda than it is for kids that do drink soda.
b. Construct a 99% confidence interval for the difference in the probabilities of getting a fracture for non-cola drinking and cola drinking kids. In one or two sentences, interpret this interval for someone who has never taken a statistics course.