In a sample of the driving records of 137 young adult males who underwent treatment for substance abuse in a Toronto clinic, the mean accident rate after treatment was 0.068, with a standard deviation of 0.223 (based on data from "Does Treatment of Substance Abuse Improve Driving Safety? A Preliminary Evaluation," by Mann et al., Addiction Research Foundation). Suppose a competing clinic claims that those who complete its substance-abuse program have better driving records. In a random sample of 20 of its past clients, the mean accident rate after treatment was 0.061, with a standard deviation of 0.210.
a. At the 0.05 level of significance, test the claim that the past clients of both clinics have the same mean accident rate. Based on this result, is the competing clinic entitled to make the assertion that it does?
b. Construct a 95% confidence interval for the difference between the mean accident rates for the client groups from the two clinics