I live out in the country or what some people call rural.  Do you live in a rural area?
No I live in a city but I do have friends living outside towns and cities.
Is most of America living in rural settings?
Yup more than 50% of the population is living in rural communities 
I was thinking that.  Isn't it cheaper to live in a rural setting than in a big city?
Yea pretty much, predominantly rural regions have less than 15 percent of the on going inflation rate.
I imagine that life is slower and more relaxed in rural areas as well too, right?
I am not sure but I can see why since population density is less than 150 people per square kilometre. 
What is the population density in a city?  I am just asking so I can reference the difference between the two.
Population density
Population density (in agriculture: standing stock and standing crop) is a measurement of population per unit area or unit volume; it is a quantity of type number density. It is frequently applied to living organisms, and most of the time to humans. It is a key geographical term. In simple terms population density refers to the number of people living in an area per kilometer square.
Biological population densities.
Population density is population divided by total land area or water volume, as appropriate.
. Typically, it has referred to the population living outside settlements of 1,000 or fewer inhabitants. The current definition states that census rural is the population outside settlements with fewer than 1,000 inhabitants and a population density below 400 people per square kilometre (Statistics Canada, 2007).
North America United States.
84% of the United States' inhabitants live in suburban and urban areas, but cities occupy only 10 percent of the country. Rural areas (villages) occupy the remaining 90 percent. The U.S. Census Bureau, the