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 26 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 104 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.
◦ Use one detergent brand (Brand A). Put 52 loads in hot water and 52 loads in cold water, and compare the results.
◦ Consider all eight combinations of brand and temperature (e.g., A-hot, A-cold, B-hot, B-cold, etc.). Randomly assign 13 loads to each of the eight combinations.
◦ For each of the 104 loads, randomly select one of the detergent brands and randomly select hot or cold water.
◦ Randomly select two brands (say, A and B) and wash 26 loads in with each brand in cold water. Use hot water in all loads washed by the remaining two brands (say, C and D).
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