Since the question mentioned boot.ci, I thought I would try to replicate the results of @knrumsey with the boot package.

A couple of notes. I copied my general code for using boot.ci with a function from here (with the caveat that I am the author of the code).

The results are similar to those of @knrumsey.

I don't know what the difference is between the accelerated intervals in the original answer and the bias-corrected accelerated intervals that boot.ci uses.

set.seed(42)
n <- 30 #Sample size
x <- round(runif(n, 0, 100))

library(boot)

Function = function(input, index){
                    Input = input[index]
                    Result = var(Input)/mean(Input)^2 - 1/mean(Input)
                    return(Result)}

Boot = boot(x, Function, R=10000)

hist(Boot$t[,1])

boot.ci(Boot, conf = 0.95, type = "perc")

   ### BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
   ### Based on 10000 bootstrap replicates
   ###
   ### Intervals : 
   ### Level     Percentile     
   ### 95%   ( 0.1021,  0.3521 )  

boot.ci(Boot, conf = 0.95, type = "bca")

   ### BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
   ### Based on 10000 bootstrap replicates
   ###
   ### Intervals : 
   ### Level       BCa          
   ### 95%   ( 0.1181,  0.3906 )  

Since the question mentioned boot.ci, I thought I would try to replicate the results of @knrumsey with the boot package.

A couple of notes. I copied my general code for using boot.ci with a function from here (with the caveat that I am the author of the code).

The results are similar to those of @knrumsey.

I can't confirm that the 'perc' and 'bca' methods are the same as those used in the original answer.

set.seed(42)
n <- 30 #Sample size
x <- round(runif(n, 0, 100))

library(boot)

Function = function(input, index){
                    Input = input[index]
                    Result = var(Input)/mean(Input)^2 - 1/mean(Input)
                    return(Result)}

Boot = boot(x, Function, R=10000)

hist(Boot$t[,1])

boot.ci(Boot, conf = 0.95, type = "perc")

   ### BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
   ### Based on 10000 bootstrap replicates
   ###
   ### Intervals : 
   ### Level     Percentile     
   ### 95%   ( 0.1021,  0.3521 )  

boot.ci(Boot, conf = 0.95, type = "bca")

   ### BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
   ### Based on 10000 bootstrap replicates
   ###
   ### Intervals : 
   ### Level       BCa          
   ### 95%   ( 0.1181,  0.3906 )  

Since the question mentioned boot.ci, I thought I would try to replicate the results of @knrumsey with the boot package.

A couple of notes. I copied my general code for using boot.ci with a function from here (with the caveat that I am the author of the code). It's a little verbose for this application, but I think it's easily generalizable. I added a variable y in the mix, which isn't used for anything, but allows the data frame with x to be returned as a data frame. (Usually, you'd be working with a data frame already).

The results are similar to those of @knrumsey.

I don't know what the difference is between the accelerated intervals in the original answer and the bias-corrected accelerated intervals that boot.ci uses.

set.seed(42)
n <- 30 #Sample size
x <- round(runif(n, 0, 100))

y = 1:n

Data = data.frame(x, y)

library(boot)

Function = function(input, index){
                    Input = input[index,]
                    Result = var(Input$x)/mean(Input$x)^2 - 1/mean(Input$x)
                    return(Result)}

Boot = boot(Data, Function, R=10000)

hist(Boot$t[,1])

boot.ci(Boot, conf = 0.95, type = "perc")

   ### BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
   ### Based on 10000 bootstrap replicates
   ###
   ### Intervals : 
   ### Level     Percentile     
   ### 95%   ( 0.1021,  0.3521 )  

boot.ci(Boot, conf = 0.95, type = "bca")

   ### BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
   ### Based on 10000 bootstrap replicates
   ###
   ### Intervals : 
   ### Level       BCa          
   ### 95%   ( 0.1181,  0.3906 )  

Since the question mentioned boot.ci, I thought I would try to replicate the results of @knrumsey with the boot package.

A couple of notes. I copied my general code for using boot.ci with a function from here (with the caveat that I am the author of the code).

The results are similar to those of @knrumsey.

I don't know what the difference is between the accelerated intervals in the original answer and the bias-corrected accelerated intervals that boot.ci uses.

set.seed(42)
n <- 30 #Sample size
x <- round(runif(n, 0, 100))

library(boot)

Function = function(input, index){
                    Input = input[index]
                    Result = var(Input)/mean(Input)^2 - 1/mean(Input)
                    return(Result)}

Boot = boot(x, Function, R=10000)

hist(Boot$t[,1])

boot.ci(Boot, conf = 0.95, type = "perc")

   ### BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
   ### Based on 10000 bootstrap replicates
   ###
   ### Intervals : 
   ### Level     Percentile     
   ### 95%   ( 0.1021,  0.3521 )  

boot.ci(Boot, conf = 0.95, type = "bca")

   ### BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
   ### Based on 10000 bootstrap replicates
   ###
   ### Intervals : 
   ### Level       BCa          
   ### 95%   ( 0.1181,  0.3906 )