A sewage treatment plant located along a river reported a chemical spill which may have released mercury into the river. The local environmental regulatory agency requires that such spills be monitored, and any spill that results in a long term mercury level above 2.3 #311 {micrograms per liter} requires the party at fault to pay a large fee. A random sample of 51 measurements showed a mercury reading near the treatment plant to have a sample mean of 2.43 pgfL with a sample standard deviation of 0.71 ygr'L. To decide if they should pay the fee, the treatment plant performs a hypothesis test. {a} [1 mark] Define the parameter of interest using the correct notation. Then, state the null and altemative hypotheses for this study. [in] [1 mark] Calculate the observed value of the test statistic. State the distribution {and degrees of freedom if needed] it follows. (c} [0.5 marks] Compute the pvalue or provide a range of appropriate values for the p-value. [d] [0.5 marks] Using your p-value. state the strength of evidence against H\". (Use the setup from Question 2 and your solutions from parts (a) to (d).) (e) [1 mark] Using the significance level a = 0.025, state your conclusions about if the treatment plant will pay the fee. (f) [1 mark] Using the specifics of this question (but not necessarily your conclusion from part (d), describe what would happen if a Type I error is made