Question

The manager of the public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent $\text{A}$ and Detergent $\mathrm{B}$, in cleaning the towels that are used daily.

As each dirty down is turned in, it is placed into the only washing machine on the premises.

When the washing machine contains $20$ towels, the manager flips a coin to determine whether Detergent $\text{A}$ and Detergent $\mathrm{B}$ will be used for that load.

The cleanliness of the load of towels is rated on the scale of $1$ to $10$ by a person who does not know which detergent was used.

The manager continues his experiment for days.

Which of the following best describes the manager's study $?$

• A. A completely randomized design.
• B. A randomized block design with Detergent $\text{A}$ and Detergent $\mathrm{B}$ as a block.
• C. A randomized block design with the washing machine as the block.
• D. A matched pair design with Detergent $\text{A}$ and Detergent $\mathrm{B}$ as the pair.
• E. An observational study.

Answer 1

The correct option is A

A completely randomized design.

Step-1: Explanation for the correct answer:

Option $\mathbf{\left(}\mathbf{A}\mathbf{\right)}$:

The manager's study is a completely randomized design because the treatments are assigned completely at random.

The experimental units are not grouped into the block.

The flipping of a coin determines which type of detergent to be used.

The treatment conditions are same person rating the cleanliness and the same washing machine used.

Step-2: Explanation for the incorrect answer:

Since the experimental units are not grouped into blocks, option $\mathbf{\left(}\mathbf{B}\mathbf{\right)}$ is incorrect.

Since the experimental units are not grouped into blocks, option $\mathbf{\left(}\mathbf{C}\mathbf{\right)}$ is incorrect.

Since each detergent has an equal chance of being selected, it is not a matched pair design. So, option $\left(\mathrm{D}\right)$ is incorrect.

Since the treatment condition are applied by random assignment, it is not an observational study. So option $\left(\mathrm{E}\right)$ is incorrect.

Hence, the correct option is $\mathbf{\left(}\mathbf{A}\mathbf{\right)}$.