When a set of data are binomial I have a lot of methods available to me (Wilson score interval, Wilson score interval with continuity correction, Jeffreys interval, Clopper-Pearson interval, Agresti-Coull Interval) other than the standard Wald interval estimation method (see Interval Estimation for a Binomial Proportion Author(s): Lawrence D. Brown, T. Tony Cai and Anirban DasGupta).
However, I can't use these methods for data that is itself proportional in the sense of it sitting in [0,1].
For example consider a sample of n respondents, giving a score for a question X as:
r_1 = 0.4 r_2 = 0.3 ... r_n = 0.2
How would I calculate the confidence interval for a mean based on this data? Is there any way other than bootstrapping?