Suppose we wish to test the mathematical aptitude of grade school children. One question that we may have is if higher grade levels have different mean test scores. A simple random sample of 27 third graders is given a math test, their answers are scored, and the results are found to have a mean score of 75 points with a sample standard deviation of 3 points. A simple random sample of 20 fifth graders is given the same math test and their answers are scored. The mean score for the fifth graders is 84 points with a sample standard deviation of 5 points. What is a 95% confidence interval for the difference in mean test scores between the populations of third graders and fifth graders