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A cost-benefit analysis is the best method of demonstrating savings using the average cost of a problem and intervention because it compares the costs of the intervention with the benefits gained from it. This analysis helps quantify both the costs and benefits in monetary terms, allowing for a direct comparison to assess whether the intervention is cost-effective. By calculating the net savings or benefits resulting from the intervention, stakeholders can make informed decisions about the value and impact of the intervention.

In contrast:

- An efficacy study focuses on determining whether the intervention works under ideal circumstances but does not provide a comprehensive economic assessment.

- A product evaluation assesses the quality and performance of a product but does not specifically address cost savings related to a problem and intervention.

- A cost-effective analysis compares the costs of different interventions to achieve the same outcome but may not directly quantify savings based on the average cost of a problem and intervention.