In the assignment it says that we should expect a few hundred private companies per year, but according to our data we are getting less than 10 per year. When I downloaded the data from WRDS, I kept most of the defaults (except for the date variable option). Should we change one of these options? Or is there another exchange code that is private?

Exchange codes are found on WRDS and also for your convenience on Canvas. If you are not getting any exchange 0-3 companies, you are probably using CRSP/Compustat Merged (CCM) rather than Compustat data. Make sure you are using Compustat, you should typically be getting a couple hundred companies per fiscal year.