One of the hazards of strip mining is that water passing through the mine’s “tailings” (the piles of discarded material) is often very acidic and contains high concentrations of metal ions, such as Pb2+ and Cd2+.
(a) Suppose you are involved in a study to determine whether a strip mine is responsible for the high concentrations of metal ions in a local stream. Your first task is decide on where to collect samples of sediment. Shown below is a map of the area from which you are planning to collect samples. You are limited to six sampling locations due to time and budget constraints. Which of the six sampling strategies (random, systematic, judgmental, systematic/judgmental, stratified or convenience) would you use to select your sites? Please note that more than one strategy may be appropriate, but that some strategies are clearly inappropriate. Show, using dots (•), where you might place these sampling locations, being sure that your locations are consistent with your sampling strategy.
(b) Four replicate 1-g samples of sediment are collected from a single location and analyzed for Cd, giving results of 5.09, 6.29, 6.64 and 4.63 ppb. Assuming that sampling is the only significant source of indeterminate error, report the percent relative standard deviation due to sampling.
(c) The next step in the sampling plan is to determine the minimum sample size needed to obtain results of acceptable precision. Although the concentration of Cd may vary significantly from location-to-location, the soil at any single location is reasonably homogeneous. What size samples should be collected if you want the relative standard deviation due to sampling to be 5%?
(d) The final step in the sampling plan is to determine the number of samples to collect at each location. Assuming that you are looking to achieve results with a relative error of no more than ±3%, what is the minimum number of samples that you should collect from each location?
(e) In question (b) we assumed that sampling was the only important source of indeterminate error. Briefly explain how you would verify that the method does not significantly contribute to the indeterminate error.
