A consumer agency wants to determine which of two laundry detergents, A or B, cleans better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale of 1–10, with 1 being the least clean to 10 being the most clean. The mean rating for detergent A is found to be significantly less than the mean rating for detergent B.
Answer
A
Inferences can be made about the population of fabric from which the pieces were chosen, and the conclusion can be made that detergent B cleans better than detergent A for all fabric.
B
Inferences cannot be made about the population of fabric from which the pieces were chosen; however, the conclusion can be made that detergent B cleans better that detergent A for these 50 pieces of fabric.
C
Inferences can be made about the population of fabric from which the pieces were chosen; however, the conclusion cannot be made that detergent B cleans better than detergent A for these 50 pieces of fabric.
D
Inferences cannot be made about the population of fabric from which the pieces were chosen; and the conclusion cannot be made that detergent B cleans better than detergent A for these 50 pieces of fabric.
Explanation
The pieces were randomly assigned to detergents, so the comparison supports the conclusion that detergent B cleaned these 50 pieces better than detergent A. But the pieces were not stated to be randomly sampled from a larger population of fabric, so the results cannot confidently be generalized to that population. Thus, choice B is correct.
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