Logos, Pathos, or Ethos?

According to a survey conducted by the U. S. Department of Health, people who observe a vegetarian diet live longer than people who do not.

Logos

Explanation:

Logos pathos and ethos are greek words that make reference to a different way to persuade people into doing or into believing something, in this case the sentence is trying to persuade the reader into being a vegetarian, and it does it by appealing to reason, providinf facts and data that the U. S Department of Health provided, that state that people with vegetarian live longer than people who do not, this is an appeal to the reason and the logic of people that tries to persuade people to become vegetarian.

Logos because it is using statistics and facts to back it up.