A new drug has been developed for treatment of a certain disease. A group of 500 patients suffering from the disease were treated with the new drug. Another group of 500 patients were treated with an alternative drug. At the end of two weeks, 360 of the patients receiving the new drug recovered, while 220 of those taking the alternative drug recovered. Construct a 99% confidence interval for the difference in the true proportion of patients who might be expected to respond to the two drugs.