A mathematics test is given to a class of 50 students randomly selected from high school 1 and also to a class of 45 students randomly selected from high school 2. For the class at high school 1, the sample mean is 75 points, and the sample standard deviation is 10 points. For the class at high school 2, the sample mean is 72 points, and the sample standard deviation is 8 points. Construct a 95% confidence interval for the difference in the mean scores. What assumptions are necessary?