Final answer:
The objective that leads to a test of the efficiency of an organization's use of labor resources is reducing labor costs. This involves assessing the cost-effective use of labor in relation to its output, which is influenced by factors like training effectiveness and technology use.
Step-by-step explanation:
Among the possible engagement objectives listed, the one that would lead to a test of the efficiency of an organization's use of labor resources is reducing labor costs. This is because evaluating the efficiency of labor involves assessing how well labor resources are managed in terms of cost and output. A study by Arthur, Bennett, Edens, and Bell in 2003 can be connected to this objective as it showed the effectiveness of organizational training on productivity, which is a factor in labor efficiency.
Scientific management also had the goal to increase workers' efficiency, which is directly related to the use of labor resources. As wages rise, for example, to $24 an hour, firms may look to shift towards production technology that utilizes more machinery over labor to reduce costs, such as the use of three machines and fewer labor hours. This reflects an effort to balance between labor costs and productivity to achieve greater labor efficiency.