Question

Which of the following statements about the measurements of the two students is correct?

A) The first student's measurement is more accurate.
B) The second student's measurement is more accurate.
C) Both students' measurements are equally valid.
D) Neither student's measurement is valid.

Answer 1

The information provided does not specify which student's measurements are more accurate; accuracy is determined by how close a measurement is to the true value. Precision, denoting consistency of measurements, is different from accuracy. For hypothesis testing on matched samples, paired observations are compared, and precision of instruments affects the granularity of measurements.

Step-by-step explanation:

From the information given, we cannot determine which student's measurements are more accurate without specific data. Accuracy in measurements refers to how close a measurement is to the correct value. If student one's measurements are all close to the actual value, they are considered accurate. If student two's measurements are closer to the actual value than student one's measurements, then student two's measurements are more accurate.

However, if both sets of measurements are equally close to the true value, then both students' measurements are equally valid. It is important to note that precision and accuracy are not synonymous. Precision refers to the consistency of repeated measurements, while accuracy refers to how close those measurements are to the actual value. A measurement can be precise without being accurate if all the measurements are consistently wrong.

When performing a hypothesis test on matched or paired samples, it is true that two measurements are drawn from the same pair of individuals or objects, and two sample means are compared to each other. As for the measuring devices, the ruler with millimeter markings is more precise because it reports more digits, allowing for a more detailed measurement.

Answer 2

The accuracy and precision of the measurements determine which statement is correct.

Step-by-step explanation:

The correct statement about the measurements of the two students depends on the concept of accuracy and precision. Accuracy refers to how close a measurement is to the correct value, while precision refers to how consistent and exact a set of measurements are. If the first student's measurements are consistently close to the correct value, then their measurements are more accurate. If the second student's measurements are consistently close to the correct value, then their measurements are more accurate. If both students' measurements are consistently close to the correct value, then both measurements are equally valid. If neither student's measurements are consistent or close to the correct value, then neither measurement is valid.