I'd like to calculate proportion confidence intervals for a labor economics survey of 2000 people, but the subpopulations I'm looking at are often 10 or fewer people. I'm not sure if it's appropriate to assume normality and was looking for some non-parametric way to calculate proportions.
Within the survey, I'm looking at workers who are urbanized, skilled, or self-employed. When broken down by year, it narrows to a small N by sub-population. The histograms are often heavily skewed, depending on the variables used.
So, for instance, let's say I have data (in R)
year <- c(2000, 2001, 2002) total <- c(1000, 1000, 1000) selfemployed <- c(4, 5, 6) test <- data.frame(year, total, selfemployed)
And I want to estimate some form of upper and lower-bound estimates of the number of self-employed in the population, what is a good method? This is not for regression or modeling, just descriptive statistics. I saw a discussion of bootstrapping methods here but am unsure the best method. Thanks, and please let me know if I can make this question more clear.