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

question 38

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.

---

Definitions:

Utility Functions

Represent mathematical models that quantify an individual's preference for certain bundles of goods or services under conditions of scarcity.

Public Good

An item or resource that cannot be withheld from anyone and whose consumption by one individual does not diminish its accessibility to others, characterized by being both non-excludable and non-rival.

Private Good

A product or service that is typically consumed by the purchaser and cannot be used or consumed by others.

Utility Function

A mathematical representation in economics depicting the relationship between consumption choices and levels of satisfaction or happiness.