Prediction Value vs Measurement Value: Do They Agree Well?

Do the prediction value of y = 2.45 ± 0.72 cm and the measurement value of y = 3.36 ± 0.03 cm agree well?

True

False

Answer:

False

In mathematical terms, prediction values are estimates that fall within a certain expected range, often given as a value plus-or-minus a margin of error. The prediction value in this case is y = 2.45 ± 0.72 cm, while the measurement value is y = 3.36 ± 0.03 cm. To determine if these values agree well, we need to compare their ranges.

The range of the prediction value is from (2.45 - 0.72) cm to (2.45 + 0.72) cm, which is from 1.73 cm to 3.17 cm. On the other hand, the range of the measurement value is from (3.36 - 0.03) cm to (3.36 + 0.03) cm, which is from 3.33 cm to 3.39 cm.

Since the range of the measurement value (3.33 cm to 3.39 cm) does not overlap with the range of the prediction value (1.73 cm to 3.17 cm), it indicates that the prediction value and the measurement value do not agree well. Therefore, the answer to the question is false.