Update #1

In order to be able to visually see if there is possibly a correlation between population density and the percentage of days of Ozone exceedance I created a map showing the two data files.  For the population density, I chose a graduated quantity symbology which would show lower population densities in lighter colors and higher population densities in darker colors.  For the ozone exceedance, I chose to use a proportional symbol so that I could see which counties had higher occurrences and which had lower in relation to their respective population densities.  Before using the data files, I had expected that counties that had a higher population density would probably have higher occurrences of ozone exceedance days because high densely populated areas are normally cities, which I would expect to produce more pollutants than rural areas and thus have a larger number of asthma cases. With that being said, you cannot determine whether there is a significant relationship between two variables solely based on visual analysis, so I will have to use other analysis tools in order to determine if what I am seeing is significant or due to chance.