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 8 in-state applicants results in a SAT scoring mean of 1132 with a standard deviation of 56. A random sample of 17 out-of-state applicants results in a SAT scoring mean of 1238 with a standard deviation of 52. Using this data, find the 98% 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 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.