An appliance manufacturer is interested in determining whether the brand of laundry detergent used affects the average amount of dirt removed from standard household laundry loads. An
Experiment is set up in which 12 laundry loads are randomly assigned to each of four laundry
Detergents-- Brands A, B, C, and D. (A total of 40 loads in the experiment.)A manufacturer of
Brand A claims that the design of the experiment is flawed. According to the manufacturer, Brand
A is better in cold water than in hot water. If all 48 loads in the above experiment were run in hot
Water, the results will be biased against Brand A. Explain how to redesign the experiment so that
The main effects of both brand and water temperature (hot or cold)on amount of dirt removed,
And their possible interaction, can be investigated.
A) For each of the 48 loads, randomly select one of the detergent brands and randomly select hot or cold water.
B) Randomly select two brands (say, A and B) and wash 12 loads in with each brand in cold water. Use hot water in all loads washed by the remaining two brands (say, C and D).
C) Use one detergent brand (Brand A). Put 24 loads in hot water and 24 loads in cold water, and compare the results.
D) Consider all eight combinations of brand and temperature (e.g., A-hot, A-cold, B-hot, B-cold, etc.). Randomly assign 6 loads to each of the eight combinations.

Question

An appliance manufacturer is interested in determining whether the brand of laundry detergent used affects the average amount of dirt removed from standard household laundry loads. An
Experiment is set up in which 12 laundry loads are randomly assigned to each of four laundry
Detergents-- Brands A, B, C, and D. (A total of 40 loads in the experiment.)A manufacturer of
Brand A claims that the design of the experiment is flawed. According to the manufacturer, Brand
A is better in cold water than in hot water. If all 48 loads in the above experiment were run in hot
Water, the results will be biased against Brand A. Explain how to redesign the experiment so that
The main effects of both brand and water temperature (hot or cold)on amount of dirt removed,
And their possible interaction, can be investigated. 
A) For each of the 48 loads, randomly select one of the detergent brands and randomly select hot or cold water.
B) Randomly select two brands (say, A and B) and wash 12 loads in with each brand in cold water. Use hot water in all loads washed by the remaining two brands (say, C and D).
C) Use one detergent brand (Brand A). Put 24 loads in hot water and 24 loads in cold water, and compare the results.
D) Consider all eight combinations of brand and temperature (e.g., A-hot, A-cold, B-hot, B-cold, etc.). Randomly assign 6 loads to each of the eight combinations.

Quizplus · Accepted Answer

To properly investigate the effects of both detergent brand and water temperature on the amount of dirt removed, as well as their interaction, it's necessary to test every combination of brand and temperature. Option D achieves this by considering all eight possible combinations (four brands each at two temperatures) and assigning an equal number of loads to each combination. This design allows for the analysis of the main effects of both brand and temperature, along with their interaction effect.

An Appliance Manufacturer Is Interested in Determining Whether the Brand