Two random samples were selected independently from populations having normal distributions. The statistics given below were extracted from the samples. Complete parts a through c. X1 = 41.6 X2 = 30.5 a. If 61 =5 and 62 = 3 and the sample sizes are n, = 50 and n2 = 50, construct a 90% confidence interval for the difference between the two population means. The confidence interval is 9.74 S (H1 - H2) $ 12.46. (Round to two decimal places as needed.) b. If 61 = 02, $1 = 5, and s2 = 3, and the sample sizes are n, = 10 and n2 = 10, construct a 90% confidence interval for the difference between the two population means. The confidence interval is 7.90 S (H1 - H2) $ 14.30 (Round to two decimal places as needed.) c. If 61 # 62, $1 =5, and $2 = 3, and the sample sizes are n, = 10 and n2 = 10, construct a 90% confidence interval for the difference between the two population means. The confidence interval is |s (H1 - 12) s (Round to two decimal places as needed.)