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 versus . Which of the following describes a Type II error?

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  versus . Which of the following describes a Type II error?

BlackTom AI · Accepted Answer

The question concerns Type I and Type II errors in the context of EPA emission monitoring. The setup defines an acceptable emission level at no more than 5 parts per million (5 ppm). The hypotheses are: H0: emissions ≤ 5 ppm versus Ha: emissions > 5 ppm.

Option presented: 'The EPA fails to find evidence that emissions exceed acceptable limits when, in fact, they do exceed acceptable limits.'

Analysis of this option:
- This statement describes a failure to detect a true problem. In statistical terms, failing to reject H0 when H0 is false is a Type II error. Since the true state is emissions > 5 ppm (the alternative is true) but we do not reject the null, we have committed a Type II error.
- The key elements are: (1) the null hypothesis is actually false (emissions exceed 5 ppm), and (2) the decision is to fail to reject the null. The consequence is that the pollutant is not penalized or required to clean up despite exceeding the limit.

Why this option is correct in the context:
- It precisely captures the essence of a Type II error: the failure to detect a true violation of the regulation.

Why there are no competing options to evaluate here:
- The provided data includes only one answer choice. Without alternative statements to compare, we cannot assess other potential misconceptions (such as confusing Type II with a Type I error, or mischaracterizing the direction of the test).

Additional context that clarifies the concept:
- Type I error would be rejecting H0 when H0 is true (falsely declaring a violation when emissions are within the limit).
- Type II error corresponds to a false negative: thinking everything is fine when it isn’t.
- The probability of a Type II error depends on the true emission level beyond 5 ppm and the test’s power, which is influenced by sample size and variability.

类似问题

A Type II error occurs when:

A Type II error occurs when:

What is the probability of making a Type II Error in a test?

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