set.seed(42)

incumbant <- c(7.3, 8.4, 8.4, 8.5, 8.7, 9.1, 9.8, 11.0, 11.1, 11.9)
proposed  <- c(17.3, 17.9, 19.2, 20.3, 20.5, 20.6, 21.1, 21.2, 21.3, 21.7)
mean(proposed) / mean(incumbant)

for (i in 1:M) {
    rs[i] <- mean(sample(proposed, replace=T)) - 2 * mean(sample(incumbant, replace=T))
}

ci.hall <- 2 * (mean(proposed)-2*mean(incumbant)) - rev(quantile(rs,prob=c(0.05, 0.95)))
names(ci.hall) <- rev(names(ci.hall))
ci.hall

   5%   95%
-0.29  2.95

sum(rs>=0)/M

[1] 0.8915