Final answer:
The just-noticeable difference (JND) is the smallest weight difference that can be detected between two weights, which scales with the magnitude of the weights according to Weber's Law. For a one-pound bag of rice, the JND may be 0.2 pounds, whereas for a 20-pound bag, the proportional JND may be around 4 pounds, reflecting the law's principle that the JND is a function of the stimulus intensity.
Step-by-step explanation:
The smallest detectible weight difference between a one-pound bag of rice and a larger bag is the point at which an individual can perceptibly notice a change in weight when compared with the one-pound standard. This is referred to as the just-noticeable difference (JND), which is the minimum amount of change needed for a person to detect a difference. Similarly, for a 20-pound bag, the JND would be the smallest difference in weight that can be detected when compared to the 20-pound standard. This differs from detecting a change between a 20-pound and 21-pound bag, which may not be as noticeable due to the Weber's Law. According to Weber's Law, the JND is not a fixed quantity, but rather a proportional value that is dependent on the initial stimulus magnitude.
For instance, if the initial JND for a one-pound bag is determined to be 0.2 pounds (20 percent of the starting weight), according to Weber's Law, the JND for a 20-pound bag would also be 20 percent, which means the difference would be about 4 pounds. Therefore, while an individual can discern a 0.2-pound difference when comparing 1 and 1.2-pound bags, they would need to compare the 20-pound to a 24-pound bag to notice a similar proportional difference. Essentially, the theory predicts that as the stimulus becomes larger, the JND also increases in a manner directly proportional to the magnitude of the stimulus.