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

You can calculate so called simultaneous confidence intervals for multinomial proportions, and see if they are too wide for your purposes.
In R, it can be done like this (data contains the numbers of the respondents from the 6 categories you mentioned):
if(!require(DescTools)){
    install.packages("DescTools")
    library(DescTools)
}
data <- c(14, 52, 90, 39, 17, 288)
MultinomCI(data)

Output:
A matrix: 6 × 3 of type dbl
est     lwr.ci  upr.ci
0.028   0.000   0.0719399
0.104   0.062   0.1479399
0.180   0.138   0.2239399
0.078   0.036   0.1219399
0.034   0.000   0.0779399
0.576   0.534   0.6199399

