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 68.4 inches with a standard
deviation of 2.46 inches. A random sample of 17 non-American students had a mean height of 65.1 inches with a standard deviation of 2.96
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.