Final answer:
An investigation of a variance should be initiated if the anticipated benefits exceed the expected costs. This principle is widely used in cost-benefit analysis across different economic scenarios, from evaluating crime-reduction programs to comparing grading practices in academia.
Step-by-step explanation:
The question pertains to the concept of variance investigation within an economic analysis context, specifically relating to the identification and action on cost-benefit analysis.
An investigation of a variance should be undertaken if the anticipated benefits are greater than the expected costs. This principle is applicable in various economic analyses, such as assessing the efficiency of crime-reduction programs, determining education funding, or even evaluating grading systems in academic settings.
Utilizing cost-benefit analysis allows decision-makers to compare the extra costs and benefits associated with a decision. This analytical method helps in selecting the most efficient option, which could be regarding the allocation of resources in reducing pollution, crime, or setting academic standards.
The example provided from a mathematical perspective involves testing whether there is a significant difference in the variances of grades given by two instructors, which could be evaluated using statistical hypothesis testing at a given level of significance.