lines = 'Noise Duration Experience
0  11.5 4
0  9.5 7
20 12.0 3
20 13.0 2
40 15.0 11
40 16.0 8
60 20.0 5
60 19.0 7
80 28.0 8
80 27.0 10'
con = textConnection( lines )
DF = read.table( con, header=TRUE )
close(con)

DF$Noise = as.factor( DF$Noise )

compute_statistic = function( DF ){
    #
    # Computes the statistic as discussed in the solutions.
    #
    noise_groups = unique( DF$Noise )
    nng = length(noise_groups)

    S = 0.
    for( ng in 1:nng ){
        mask = DF$Noise == noise_groups[ng]
        df = DF[mask,]
        S = S + sum( DF$Duration * DF$Experience )
    }
    return(S)
}

# Next lets apply a permutation test:
#
S = compute_statistic( DF ) # the value of S under the original ordering

set.seed(1234)
B = 100 # the sumber of bootstraps to run
all_Ss = rep( NA, B ) # the bootstrap values of the F_1
for( bi in 1:B ){
    DF$Duration = sample(DF$Duration) # reorder the labels
    all_Ss[bi] = compute_statistic( DF )
}

plot( density( all_Ss ), xlab="statistic", main="" )
grid()
abline(v=S, col='red')

alpha = sum( all_Ss >= S ) / B
print( sprintf("Permutation Bootstrap (B= %d): prob. type I error: %10.6f", B, alpha) )