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 18 American students had a mean height of 69.9 inches with a standard deviation of 2.79 inches. A random sample of 12 non-American students had a mean height of 63.8 inches with a standard deviation of 2.31 inches. Determine the 98% 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. Step 2 of 3 : Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.