Assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean for each of the following samples:
Sample A: 1, 1, 1, 1, 8, 8, 8, 8
Sample B: 1, 2, 3, 4, 5, 6, 7, 8
Explain why these two samples produce different confidence intervals even though they have the same mean and range.