Question

The Environmental Protection Agency is charged with monitoring industrial emissions that pollute the atmosphere and water. So long as emission levels stay within specified guidelines, the EPA does not take action against the polluter. If the polluter is in violation of the regulations, the offender can be fined, forced to clean up the problem, or possibly closed. Suppose that for a particular industry the acceptable emission level has been set at no more than $5$parts per million ($5$ppm). The null and alternative hypotheses are $H_0$role="math" localid="1650298159260" $:\mu =5$versus $H_a=\mu >5$. Which of the following describes a Type II error?

(a) The EPA fails to find evidence that emissions exceed acceptable limits when, in fact, they are within acceptable limits.

(b) The EPA concludes that emissions exceed acceptable limits when, in fact, they are within acceptable limits.

(c) The EPA concludes that emissions exceed acceptable limits when, in fact, they do exceed acceptable limits.

(d) The EPA takes more samples to ensure that they make the correct decision.

(e) The EPA fails to find evidence that emissions exceed acceptable limits when, in fact, they do exceed acceptable limits.

Short answer

The Type II error is that The EPA fails to find evidence that emissions exceed acceptable limits when, in fact, they do exceed acceptable limit i.e., answer is (e).

Step-by-step solution

Given Information

We are given that the null hypotheses $H_0:\mu =5$and the alternative hypotheses $H_a:\mu >5$and

we have to find out the option that is describing the Type II error.

Reason

Now, In Type II error, The EPA is failing to reject the null hypotheses but in this null hypotheses is false.

As according to null hypotheses population mean emission is $5$but alternative population mean emission is greater than$5$.

Hence, The Type II error is that (e)The EPA fails to find evidence that emissions exceed acceptable limits when, in fact, they do exceed acceptable limits.