Help needed regarding sample size for a poll We collected data regarding the loss of subscriptions for a certain service. We know the losses to be around 1000, and we got responses from around 500 ex-members, explaining the reasons for leaving. The reasons were divided into 6 categories. Is the sample size large enough to extrapolate the sample proportions (ex: reason A/500=5%) to the overall population?
And is there any more resources that inform on this?
Thanks in advance

As the population of interest is of size $\approx 1000$ and your sample half of that population, I do not think that a binomial approximation is warranted here. Instead I would argue for modelling your data using a Hypergeometric (e.g. reason A vs. all others, and cycle through the reasons) or Multivariate hypergeometric distribution (reason A, reason B, etc. all at once).
For the first approach see this SE question including the reference mentioned.
However the problem with response bias mentioned by Henry still stands - any inference will assume that your sample stems from a random draw from that population which is unlikely to be the case. For example if one of the reasons is "the service is sending a lot of annoying emails" then anyone that left due to that reason is unlikely to respond to your survey.
