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Here's a toy data set that replicates my problem. I am interested in knowing the confidence intervals of an empirical distribution that is composed of the scores of each school at the proportion that student "A".

set.seed(1)
rows = 50
df <- data.frame(student = sample(LETTERS[1:3],rows,rep=T),
                 school = sample(c("F","G"),rows,rep=T),
                 score = sample(1:10,rows,rep=T,prob = c(rep(0.05,7),rep(0.2167,3)))
                 )
head(df)
student school score
1       A      F     3
2       B      G     9
3       B      F     9
4       C      F     1
5       A      F    10
6       C      F     8
> 

In this example: student "A" has 3 scores from school "G" and 9 scores from school "F":

> df[df$student=="A",]
   student school score
1        A      F     3
5        A      F    10
10       A      F    10
11       A      G     1
12       A      F     6
22       A      G    10
24       A      F     8
25       A      F     7
27       A      G    10
34       A      F    10
38       A      F    10
47       A      F     8

How do I generate bootstrap samples that would sample 12 scores at the correct proportion of student "A" school. I need to calculate the CI of the expected score of the average student scoring student "A"'s school proportions.

I look through the "boot" package boot function help. There is an example of stratified bootstrap but I don't get what stype is doing. I understand stype="i" but I don't understand what happens with stype="w" or "f" and how to use them.

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