Statistics Problem

Red tide” is a bloom of poison-producing algae–a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living in the area develop dangerous levels of a 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 800 μg (micrograms) of toxin per kg of clam meat in any area, clam harvesting is banned there until the bloom is over and levels of toxin in clams subside. During a bloom, the distribution of toxin levels in clams on a single mudflat is distinctly non-Normal.

a. How many samples should the DMF test in order to conclude the sampling distribution will be approximately normal if the population is distinctly non-Normal. Why?

b. Define the parameter of interest and state the appropriate hypotheses for the DMF to test.

c. Describe a Type I and a Type II error in this situation and the consequences of each.