I'm trying to understand how I would decide whether a policy actually had a meaningful impact by comparing the population itself, not samples.
An example that comes to mind is comparing the number of accidents on a specific road during $n$ months prior to enacting a law to reduce the speed on that road, to $n$ months after enacting this law.
I would think that I could use a paired t-test using biased standard deviation, since I'm looking at absolute values of the actual population, not samples, but I see a few problems with that: how would I calculate the Standard Error for the t-value if there is no error because I'm looking at the population itself? How would I calculate standard deviation, if there is no mean?
What I'm really trying to understand is: say in my pre-test I get an $x$ number of accidents and in the post-test I got a $y$ number of accidents where $0 < x < y$. How could I know if this change was statistically significant? If someone could just point me to the right direction I can study the subject. I just don't know where to look.