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12. "Red tide" is a bloom of poison-producing algae - a few different species of a class of plankton called dinoflagellates. When we en weather and water conditions cause these blooms, shellfish such as clams living in the area develop dangerous levels of paralysis-inducing toxin. In Massachusetts, the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds 790 ug (micrograms) of toxin per kg of clam meat in any area at a 10% level of significance, clam harvesting is banned there until the bloom is over and the levels of toxin the clams subside. During the bloom, the distribution of toxin levels in clams on a single mudflat is distinctly non-Normal. a. Define the parameter of interest and state appropriate hypotheses for the DMF to test 0* = 01 10 Ho: M= #790 Mg Ha:M> 790Mg + ese ge =? what does u represent? b. Because of budget constraints and the large number of coastal areas that must be tested, the DMF would like to sample no more than 15 clams from any single area. Explain why this sample size may lab lead to problems in carrying out the significance test from (a). The sample size of no more than 15 clams may lead to + 2 problems due to the C.L. T because it is less tran 30. why ? what issues ? e. Describe a Type I and at Type II error in this situation and explain possible consequences of each. Type I crow: If we reject that the level of toxin in clams is 790 when it actually is. This will lead to consequences of having no clam havesing Type 11 error: If we fail to reject that the Level of toxins in clams is 790 when it actually is?"This could lead to DMF's business to be banned for good because They would be havesing toxic clams. Discuss the impact this d The DMF is considering changing the significance level of this test to 5%. might have on error probabilities and the power of the test, and describe the practical consequences of this change It the DMF changes the significance level to 0.05 one of them would . The probabilities of error would decrease significantin and the practical consequences of having toxms in That small level of significance Level would morease