## Creating a 95% Bootstrap Confidence Interval for the sample standard deviation ### General Steps 1. Take the original sample, which has a sample size of sample_size, and treat it like the population. 2. Take a sample of size sample_size, with rep

create-bootstrap

create_bootstrap <- function (.data, num_samples, sample_size) {
  # Create "num_samples" samples, of size "sample_size", from the original population ".data"
  samples <- rerun(num_samples, sample(.data, sample_size, replace = TRUE))

  # Find the standard deviation of each dataset
  std_devs <- samples %>% map_dbl(sd)
  
  # Find the bounds of the 95% confidence interval
  interval <- std_devs %>% quantile(c(.025, .975))
  
  # Return a list containing the confidence interval and the standard deviations of each dataset.
  list(interval = interval, std_devs = std_devs)
}

### Usage ###

# The original sample
set.seed(26)
samp <- rnorm(20, mean = 10, sd = 6)

# Create the bootstrap
bootstrap <- create_bootstrap(samp, 10000, 20)

# Print the interval
bootstrap$interval

# Plot a histogram of the standard deviations to see the bootstrap distribution
hist(bootstrap$std_devs)