Two random samples were selected independently from populations having normal distributions. The following statistics were extracted from the samples:

a. If σ1 = 3 and σ2 = 2 and the sample sizes are n1 = 50 and n2 = 50, construct a 95% confidence interval for the difference between the two population means.
b. If σ1 = σ2, σ1 = 3, and σ2 = 2, and the sample sizes are n1 = 10 and n2 = 10, construct a 95% confidence interval for the difference between the two population means.
c. If σ1 ≠ σ2, σ1 = 3, and σ2 = 2, and the sample sizes are n1 = 10 and n2 = 10, construct a 95% confidence interval for the difference between the two population means.