Question

the quality - control manager of a large factory is concerned about the number of defective items produced by workers. thirty workers at the factory agree to participate in a study of three different incentive plans to help reduce the number of defective items produced. the plans will be randomly assigned to the workers so that 10 workers received each plan. the reduction in the number of defective items produced by each worker will be recorded two weeks after the plans are implemented. which of the following best describes why a completely randomized design is an appropriate design to use in this situation? a there is no blocking variable, and incentive plans will be randomly assigned to the workers. b there is no blocking variable, and the workers were selected at random. c each incentive plan is a block, and a completely randomized design is not blocked. d each plan will be randomly assigned to 10 pairs of workers who share a similar characteristic. e the number of workers participating in the study was greater than or equal to 30.

Explanation:

In a completely randomized design, treatments (in this case, incentive plans) are randomly assigned to experimental units (workers). There is no blocking variable (a variable used to create homogeneous groups). Option A correctly states that there is no blocking variable and incentive plans are randomly assigned. Option B is wrong because the workers were not selected at random (they agreed to participate). Option C is incorrect as incentive plans are not blocks in a completely randomized design. Option D describes a matched - pairs design (not completely randomized). Option E is incorrect as the number of workers (30) is just the sample size and not the reason for using a completely randomized design.

Answer:

A. There is no blocking variable, and incentive plans will be randomly assigned to the workers.