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 10 in-state applicants results in a SAT scoring mean of 1173 with a standard deviation of 38. A random sample of 15 out-of-state applicants results in a SAT scoring mean of 1076 with a standard deviation of 57. Using this data, find the 95% 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. Find the margin of error to be used in constructing the confidence interva.