Carlisle conducted an experiment to determine if the there is a difference in mean body temperature for men and women. He found that the mean body temperature for a sample of 100 men was 97.9 with a population standard deviation of 0.57 and the mean body temperature for a sample of 100 women was 98.6 with a population standard deviation of 0.55.

Assuming the population of body temperatures for men and women is normally distributed, calculate the 99% confidence interval and the margin of error for the mean body temperature for both men and women. Using complete sentences, explain what these confidence intervals mean in the context of the problem.