Question

select all that apply which statements about precision and accuracy are correct? □ the most precise measurement is closest to the accepted value. □ the accuracy of a measurement is independent of its precision. □ the most accurate measurement is closest to the accepted value. □ the most precise measurement has the smallest uncertainty.

Explanation:

1. Analyze "The most precise measurement is closest to the accepted value": Precision refers to the closeness of measurements to each other, not to the accepted value (that's accuracy). So this is incorrect.
2. Analyze "The accuracy of a measurement is independent of its precision": Accuracy is how close a measurement is to the true value, precision is how close measurements are to each other. A measurement can be accurate but not precise, precise but not accurate, etc. So accuracy and precision are independent. This is correct.
3. Analyze "The most accurate measurement is closest to the accepted value": Accuracy is defined as the closeness of a measurement to the accepted (true) value. So the most accurate measurement is indeed closest to the accepted value. This is correct.
4. Analyze "The most precise measurement has the smallest uncertainty": Precision is related to the spread of measurements. Smaller uncertainty means measurements are more tightly clustered (more precise). So the most precise measurement has the smallest uncertainty. This is correct.

Answer:

• The accuracy of a measurement is independent of its precision.
• The most accurate measurement is closest to the accepted value.
• The most precise measurement has the smallest uncertainty.