I'm getting confused by this and was wondering if someone can enlighten me:
I have a random sample consisting of 50 percentages. Each percentage can take on any value between 0% and 100% inclusive and is suppose to represent the quality of a file produced by a specific team. The desire is to provide inferential statistics - most notably basic hypothesis testing and confidence intervals regarding the quality of files produced by this team.
I am fairly confident the binomial distribution is not suitable as I have a vector of proportions, rather than a vector of passes/fails. The following thread Distribution for percentage data seems to confirm this. However, the solution gung suggested relates to continuous proportions. In my scenario, each percentage is formed by taking the proportion of correct answers from 15 questions. So I don't have continuous proportions but rather discrete proportions. In addition, it is possible to obtain a percentage of 100% or 0% (because all 15 questions were correct or were incorrect).
This makes me wary about using a beta distribution.
I should add that each of the 15 questions is binary. So effectively each percentage is the mean of a binomial variable that takes on the value 1 (correct) or 0 (correct) across 15 trials. This is similar (I think) to the following post Statistical tests when each variable in a sample is a percentage though I admit I struggled to grasp the underlying message from the post.
Should I still work with the beta distribution?
Does each percentage being the mean of a binomial variable allow me to consider the sampling distribution of the percentages as binomial?
Is it easier/better to simply work with the count of correct questions instead? So I would have a sample of 50 integers that can take values between 0-15.