The Department of Natural Resources Classifies a Fish to Be $$2.6,6.6,4.8,5.4 , \quad 5.1 , \quad 4.5,6.9 , \quad 4.9,3.7,3.8$$

Essay

The department of natural resources classifies a fish to be unsafe to eat if its
polychlorinated biphenol (PCB) concentration exceeds 5 parts per billion (ppb). A
random sample of 10 fish taken from a local lake resulted in the concentrations listed
below:
2. $$2.6,6.6,4.8,5.4 , \quad 5.1 , \quad 4.5,6.9 , \quad 4.9,3.7,3.8$$ The department if natural resources is concerned that the mean PCB concentration for
fish from this lake exceeds 5 ppb.
a) What null and alternative hypotheses should the investigators use? In a few
sentences, justify your choice of the alternative hypothesis.
b) Using a graphic technique of your choice, show that the t-procedures are
appropriate to use with these data.
c) Using your hypotheses from part (a), carry out a hypothesis test using α= 0.05
and interpret the results.
d) In the context of this study, describe a Type I and a Type II error.