Because it permits a slower and more natural rhythm of life, living in the country is supposed to be more healthy and relaxed than living in the city.
Statements
Living in the country is supposed to be more healthy and relaxed (because of the slower, more natural rhythm).
But surveys show people living in the country become ill as often and as seriously as people in the city, and they experience an equal amount of stress.
Evaluate
This looks like a Reconcile the Pivot setup, where the synthesis comes by combining the final idea with what came before the pivot word (But).
The tension between the two statements is that people think that the country is healthier and relaxed, but it seems like they're just as sick and stressed as city folk.
However, the first claim is a Causal one — living in the country permits a slower and more natural rhythm.
Goal
Maybe it will be some anti-causal synthesis, where we reconcile the Difference of country living (slower, more natural rhythm) with the Sameness of country living (just as sick and stressed), like
slower and more natural rhythm does not tend to make you healthier / more relaxed
Stay flexible, though. Whatever we can prove/support works.