Step 1 :First, we need to find the z-score that corresponds to a 99% confidence interval. The z-score for a 99% confidence interval is approximately 2.576.
Step 2 :The formula for a confidence interval is \(CI = \bar{x} ± Z * (\sigma/\sqrt{n})\), where \(\bar{x}\) is the sample mean, Z is the z-score, \(\sigma\) is the population standard deviation, and n is the sample size.
Step 3 :Substituting the given values into the formula, we get \(CI = 3.9 ± 2.576 * (0.9/\sqrt{1097})\).
Step 4 :To find the lower endpoint of the confidence interval, we calculate \(3.9 - 2.576 * (0.9/\sqrt{1097}) = 3.9 - 2.576 * 0.0271 = 3.9 - 0.07 = 3.8\) (rounded to one decimal place).
Step 5 :To find the upper endpoint of the confidence interval, we calculate \(3.9 + 2.576 * (0.9/\sqrt{1097}) = 3.9 + 2.576 * 0.0271 = 3.9 + 0.07 = 4.0\) (rounded to one decimal place).
Step 6 :So, the 99% confidence interval for the mean consumption of milk among people over age 32 is \(\boxed{(3.8, 4.0)}\) liters.