The 10% rule:
(a) In the example discussing the 10% rule, we used two hypothetical waters with pollutant concentration distributions Â (indicating that the water is in compliance) and Â (indicating that the water is impaired), respectively. Use simulation to evaluate the performance of the 10% rule by estimating the probability of making mistakes when sample size is low (n=10) and large (n=100) and discuss the implications of the poor performance.
(b) Use the function viol.sim to calculate the error rates for the impaired water (with pollutant concentration distribution Â with sample sizes n = 6, 12, 24, 48, 60, 72, 84, 96 and present the result in a plot. Repeat the same for a water that is not impaired.
(c) Write a short essay on the 10% rule, discussing the consequences of the rule in terms of the probability of making two type of mistakes â€“ declaring a water to be impaired while the water is in compliance and vice versa.