During one particular war, the U. S. military was concerned about the nutrition of its recruits. Many did not have a sufficient number of teeth to chew the food provided to soldiers. As a result, it was likely that they would be undernourished and unable to fulfill their duties as soldiers. The requirements at that time specified that a recruit must have "at least four sound double teeth, one above and one below on each side of the mouth, and so opposed" so that they could chew food. Of the 58,352 recruits who were under the age of 20, 88 were rejected for this reason. For the 43,886 recruits who were 40 or over, 3,901 were rejected. Find a 99% confidence interval for the difference in the proportions.