Chapter 8.6, Problem 61E

A small amount of the trace element selenium, from 50 to 200 micrograms (μg) per day, is considered essential to good health. Suppose that independent random samples of n₁ = n₂ = 30 adults were selected from two regions of the United States, and a day’s intake of selenium, from both liquids and solids, was recorded for each person. The mean and standard deviation of the selenium daily intakes for the 30 adults from region 1 were $\bar{y}$₁ = 167.1 μg and s₁ = 24.3 μg, respectively. The corresponding statistics for the 30 adults from region 2 were $\bar{y}$₂ = 140.9 μg and s₂ = 17.6 μg. Find a 95% confidence interval for the difference in the mean selenium intake for the two regions.