The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 9 in-state applicants results in a SAT scoring mean of 1190 with a standard deviation of 40. A random sample of 18 out-of-state applicants results in a SAT scoring mean of 1228 with a standard deviation of 36. Using this data, find the 99% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 3: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.