Question

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 1138 with a standard deviation of 29. A random sample of 17 out-of-state applicants results in a SAT scoring mean of 1219 with a standard deviation of 27. 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

Answer 1

Since , the population variances are not equal.

Now , degrees of freedom is ,

The criitcal value is ,

; From t-table

Therefore , the 98% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants is ,