The Department of Natural Resources Classifies a Fish to Be

question 5

Essay

The department of natural resources classifies a fish to be unsafe to eat if itspolychlorinated biphenol (PCB) concentration exceeds 5 parts per billion (ppb). Arandom sample of 10 fish taken from a local lake resulted in the concentrations listedbelow:
The department if natural resources is concerned that the mean PCB concentration forfish from this lake exceeds 5 ppb.
a) What null and alternative hypotheses should the investigators use?
In a fewsentences, justify your choice of the alternative hypothesis.
b) Using a graphic technique of your choice, show that the t-procedures areappropriate to use with these data.
c) Using your hypotheses from part (a), carry out a hypothesis test using ?= 0.05and interpret the results.
d) In the context of this study, describe a Type I and a Type II error.

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Definitions:

Dummy Variables

Variables created to represent categorical data with two or more categories by assigning binary values (0 or 1), allowing them to be used in regression models.

Qualitative Variables

Variables that express qualitative attributes, and are usually described by non-numeric categories or groups.

Regression Model

A statistical approach for estimating the relationships among variables, often used for prediction and forecasting.

Dummy Variables

Variables created to assign numerical values to categorical data, often used in regression analysis to include qualitative factors as independent variables.