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 99 in-state applicants results in a SAT scoring mean of 12311231 with a standard deviation of 3636. A random sample of 1919 out-of-state applicants results in a SAT scoring mean of 11611161 with a standard deviation of 3737. Using this data, find the 98%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.
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