First off, this is my first question on stats exchange. So if I mess up or anything, please let me know because I know this website is a lifesaver, and I want to spend more time on it.
Recently, I just started working for a new company as a business analyst. Lots of our data is not available to be pulled in bulk. Pulling data for all locations in the country takes about 8 hours to complete. I hope to pull a sample from our 100+ locations and estimate the mean confidence interval. Now my understanding of this is that I would need the population standard deviation to do this (https://www.dummies.com/education/math/statistics/how-to-calculate-a-confidence-interval-for-a-population-mean-when-you-know-its-standard-deviation/). However, doesn't that mean that I would need to pull data for the entire population?
However, I read this article: Formula for confidence intervals for small samples and unknown population standard deviation. To me, it seems like what I am asking to do is feasible. However, I wondered if the formula for standard deviation would be the standard deviation of the sample? Also, would N be the size of the sample or the size of the population? Thanks for the help; my memory of statistics notation is out of date right now, haha.
Also, when I'm randomly sampling, how random should I be? Our business has locations in 8 different provinces, with a wide range of membership at each location, with a mix of urban and non-urban locations. So part of me feels that randomly selecting 10 locations (or whatever that number may be) is likely not the best route.
Thank you so much for your help. I enjoy statistics, but it has been a few years since I've done many calculations. Also, it seems a lot more difficult doing statistics for a real-life situation than a question on a test or assignment.
And once more, please let me know if I made any mistakes or missteps in this question. I want to understand how to use this site.