I have two statistics from a range of districts obtained by sampling from the total district population e.g. number of doctors per district and the gender of these doctors.
Now I want to see whether there is a correlation between the number of doctors there is in a district and their gender (to know if e.g. there are fewer doctors in a district they are more likely to be male).
Could I just find the Pearson's correlation coefficient? And would the p-value (significance) make any sense? Because the statistics that I have are from a sampled so they have a confidence interval as well?