A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 12 American students had a mean height of 67.9 inches with a standard deviation of 2.08 inches. A random sample of 18 non-American students had a mean height of 64 inches with a standard deviation of 1.62 inches. Determine the 99% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students. Assume that the population variances are equal and that the two populations are normally distributed