I have data from all 3,143 counties in the USA. For each county the population is given, and there is a list of variables which are counts or averages for that county, such as the number of gas stations, number of supermarkets, number of fast food restaurants, the stroke rate, the diabetes rate, the gender, and a person's race.
Scenario 1: Can I do a paired t-test on gender and the diabetes rate, or race and diabetes rate? (To show that the average varies between males and females, or Caucasions and colored people, across the whole data set.)
I found a couple of posts here that say a t-test isn't valid if the sample populations are significantly different in size, which is definitely the case here (LA county, vs. well, almost anywhere).
Scenario 2: Is there a way of testing for a significant relationship between fast food and diabetes, using some combination of the county population, number of fast food restaurants, fast food restaurant sales per capita, and the diabetes rate? I'm looking for a significance test that can be framed as a testable hypothesis, that uses a standard significance test (and not a data mining model).