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 19 in-state applicants results in a SAT scoring mean of 1228 with a standard deviation of 39. A random sample of 11 out-of-state applicants results in a SAT scoring mean of 1168 with a standard deviation of 31. Using this data, find the 80% 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 point estimate that should be used in constructing the confidence interval.

Step 2 of 3:

Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3:

Construct the 80%80% confidence interval. Round your answers to the nearest whole number.

Answer 1

The statistical software output for this problem is :

Two sample T summary confidence interval: Hi : Mean of Population 1 H2 : Mean of Population 2 41 - 42 : Difference between two means (without pooled variances) 80% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit Hi - 2 60 12.938944 25.04164 42.968654 77.031346

Point estimate = 60

Margin of error = 17.031346

The 99% CI is : 43 to 77