What type of study is most appropriate for determining the time at which a common ancestor to humans and chimpanzees lived?

The most appropriate study for determining the time at which a common ancestor to humans and chimpanzees lived is a molecular clock analysis.

Here's why:

* Molecular clocks rely on the fact that mutations accumulate in DNA at a relatively constant rate. By comparing the genetic sequences of humans and chimpanzees, scientists can estimate the time since their lineages diverged.

* This method is particularly effective for studying evolutionary relationships between closely related species, like humans and chimpanzees, where the genetic differences are relatively small but significant.

* Other methods like the fossil record provide valuable insights but are limited by the incompleteness of the fossil record and the difficulty in accurately dating fossils.

However, it's important to note that molecular clock analysis is not without limitations. The rate of mutation can vary slightly across different regions of the genome and between different species. This variation can lead to some uncertainty in the estimated divergence time.

In summary, while the fossil record provides valuable evidence, molecular clock analysis is currently the most reliable method for determining the time of divergence between humans and chimpanzees.