In the article “Occurrence and Distribution of Ammonium in Iowa Groundwater” (K. Schilling, Water Environment Research, 2002:177–186), ammonium concentrations (in mg/L) were measured at a large number of wells in the state of Iowa. These included 349 alluvial wells and 143 quaternary wells. The concentrations at the alluvial wells averaged 0.27 with a standard deviation of 0.40, and those at the quaternary wells averaged 1.62 with a standard deviation of 1.70. Since these standard deviations are based on large samples, assume they are negligibly different from the population standard deviations. An estimate for the ratio of the mean concentration in quaternary wells to the mean concentration in alluvial wells is R = 1.62/0.27 = 6.00.

a. Since the sample means 1.62 and 0.27 are based on large samples, it is reasonable to assume that they come from normal populations. Which distribution approximates the distribution of the sample mean concentration of alluvial wells, N(0.27, 0.402) or N(0.27, 0.402/349)? Which distribution approximates the distribution of the sample mean concentration of quaternary wells, N(1.62, 1.702) or N(1.62, 1.702/143)? Explain.

b. Generate a simulated sample of sample means and of ratios of sample means. Is it reasonable to assume that the ratio R is approximately normally distributed?

c. Use the simulated sample to estimate the standard deviation of R.

d. If appropriate, use the normal curve to find a 95% confidence interval for the ratio of the mean concentrations.