Impact of static sample on CI

I'll get straight to the question first and then explain it.

In a longitudinal study, does having a static sample impact how the CI is calculated?

Math isn't my strong suit and most of this is being handled by people by people who know what they're doing but I had this question and was hoping someone could point me in the direction of some reference material. I'm looking to conduct a longitudinal study of a population N=1000. The sample will probably wind up being n=100. From what I remember of statistics that makes the CI =9.3. But isn't the calculation based on a sample being random? If it is a static sample of people wouldn't that narrow the CI?

Thank you for any help you can offer. I've been digging through some books and searching online for an answer without any luck.