The article "The Frequency Distribution of Daily Global Irradiation at Kumasi" (F. Akuffo and A. Brew-Hammond, Solar Energy, 1993:145-154) defines the daily clearness index for a location to be the ratio of daily global irradiation to extraterrestrial irradiation. Measurements were taken in the city of Ibadan, Nigeria, over a five-year period. For five months of May, the clearness index averaged 0.498 and had standard deviation 0.036. For five months of July, the average was 0.389 and the standard deviation was 0.049. Find a 95% confidence interval for the difference in mean clearness index between May and July?