The Columbus State Department of Ecology provides information on the mean lead con- tamination in parts per million (ppm) in trout in the Olentangy River basin. The date file Trout.csv contains a random sample of n = 100 trout with their lead contamination in parts per million. Please download the Trout.csv from Carmen and do the analysis for the following questions. a) Supposing the population standard deviation is known to be = 0.5 ppm, and with a large sample size of n = 100, please construct a 95% confidence interval for , the population mean lead contamination in all trout in the Olentangy River basin. You may use ZTest() or t.test() to verify your answer, but replicate the values mathematically yourself and show your work as well. b) Please interpret the confidence interval found in part (a). Explain in both statistical and scientific terms. c) Suppose the population standard deviation is unknown and the sample of n = 100 trout observations comes from a normal distribution. Please construct a 95% confidence interval for , the population mean lead contamination in all trout in the Olentangy River basin. You may use ZTest() or t.test() to verify your answer, but replicate the values mathematically yourself and show your work as well. d) Suppose the population standard deviation is unknown and the sample of n = 100 trout observations DO NOT come from a normal distribution, would you be able to construct a 95% confidence interval for , the population mean lead contamination in all trout in the Olentangy River basin using what you have learnt about constructing confidence intervals. Hint: think of what can you say about the distribution of the statistic x , where s is the sample standard deviation.