Danner and Phillips (2008) report the results from a county-wide study showing that delaying high school start times by one hour significantly reduced the motor vehicle crash rate for teen drivers in the study.

Suppose that the researchers monitored 500 student drivers for one year after the start time was delayed and found that 45 were involved in automobile accidents. Before delaying the start time, the accident rate was 12%.

a. Use a binomial test to determine whether these results indicate a significant change in the accident rate following the change in school start time. Use a two-tailed test with α = .05

b. Because the outcome of the binomial test is a borderline z-score, use both ends of the interval corresponding to X = 45 to determine whether the entire interval is in the critical region.