NT #1 The EPA maximum contaminant level (MCL) for arsenic is 10 micrograms per liter. (10,11,9/ L). You wish to test whether water has acceptable levels of arsenic, that is, below the MCL. For the following questions, consider two options: a one-sided lower tail test of H0 : ,u = 10 vs H A : ,u 10. Use a signicance level of a = .05. a) Write out what a Type I and Type II error would mean for each of the two possible one-sided tests. b) The data is in: you tested 45 water samples and found a sample mean of 10.57 pg/ L arsenic with a sample standard deviation of 2.65m} / L. Carry out hypothesis tests for both options. c) Interpret your results from part b). d) Which of the two tests do you think is the better option, and why