Question

An archaeologist uses an accelerator mass spectrometer to find the age of a buried branch. At the 68% confidence level, the spectrometer estimates that the branch was 10,000 years old with a following could the spectrometer estimate as the age of the branch at the 95% confidence level? margin of error o f 200 vears. Which of the with a margin of error of 500 years

A. 9,500 years old, with a margin of error of 500 years
B. 10,000 years old, with a margin of error of 400 years
C. 9,500 years old, with a margin of error of 50 years
D. 10,000 years old, with a margin of error of 40 years

Answer 1

To find the estimated age of the branch at the 95% confidence level, we can calculate the margin of error at this level. The margin of error at the 95% confidence level is 400 years.

Step-by-step explanation:

To estimate the age of a buried branch, an archaeologist used an accelerator mass spectrometer. At the 68% confidence level, the spectrometer estimated that the branch was 10,000 years old with a margin of error of 200 years. To find the estimated age at the 95% confidence level, we can calculate the margin of error at this confidence level.

At the 68% confidence level, the margin of error is 200 years. Since the 95% confidence level is wider, we can calculate the margin of error by multiplying it by a factor called the critical value. The critical value depends on the desired confidence level. For the 95% confidence level, the critical value is approximately 2.

Therefore, to find the margin of error at the 95% confidence level, we multiply the margin of error at the 68% confidence level by the critical value of 2. So, the margin of error at the 95% confidence level would be 2 * 200 = 400 years.