Question

Suppose that you are an inspector for the Fish and Game Department and that you are given the task of determining whether to prohibit fishing along part of the Oregon coast. You will close an area to fishing if it is determined that more than \(3 \%\) of fish have unacceptably high mercury levels. a. Which of the following pairs of hypotheses would you test: $$ H_{0}: p=0.03 \text { versus } H_{a}: p>0.03 $$ or $$ H_{0}: p=0.03 \text { versus } H_{a}: p<0.03 $$ Explain the reason for your choice. b. Would you use a significance level of 0.10 or 0.01 for your test? Explain.

Short answer

The suitable pair of hypotheses to test would be \(H_{0}: p=0.03\) versus \(H_{a}: p>0.03\). The choice of the significance level for the test would be 0.01 considering the importance of the decision.

Step-by-step solution

Identify the correct pair of Hypotheses

The appropriate pair of hypotheses would be: \(H_{0}: p=0.03\) versus \(H_{a}: p>0.03\). This is because we are interested in whether more than 3% of fish are affected, signifying \(p > 0.03\).

Identify the correct significance level

The significance level of a test indicates the risk of rejecting the null hypothesis when it is actually true. A lower significance level signifies a lower risk of making such an error. Since the decision potentially impacts the livelihood of fishermen and the conservation of the fish population, both of which are significant, it would be prudent to choose a lower significance level, i.e., 0.01, to minimize the risk of incorrectly closing the area to fishing.