In a study, the average sedimentation rate of 12 patients with carditis was calculated as X1 = 87.29 mm and S1 = 18.4 mm, while the mean sedimentation rate of 15 patients with rheumatism was calculated as X2 = 69.03 mm and S2 = 21.4 mm. Determine whether there is a difference between the mean averages of patients with carditis and rheumatism at the 5% significance level. Find the 95% confidence limits for the difference between the two population means.