library(testthat)
library(boilerplatePackage)
context("Test z.")

Set test parameters

reps <- 5000
n <- 1000
mu <- 100
sigma <- 15
Variable Description Value
reps Number of simulation replications 5000
n Sample size 1000
mu Population mean \(\left( \mu \right)\) 100
sigma Population standard deviation \(\left( \sigma \right)\) 15

Simulation

n <- rep(x = n, times = reps)
x <- lapply(
  X = n,
  FUN = rnorm,
  mean = mu,
  sd = sigma
)
std <- lapply(
  X = x,
  FUN = z,
  mu = mu,
  sigm = sigma
)

Summarize simulation

mean_x <- mean(
  unlist(
    lapply(
      X = x,
      FUN = mean
    )
  )
)
sd_x <- mean(
  unlist(
    lapply(
      X = x,
      FUN = sd
    )
  )
)
mean_z <- mean(
  unlist(
    lapply(
      X = std,
      FUN = mean
    )
  )
)
sd_z <- mean(
  unlist(
    lapply(
      X = std,
      FUN = sd
    )
  )
)

\(x\)

Item Population Sample
Mean 100 99.994397
Standard deviation 15 14.9942377

\(z\)

Item Population Sample
Mean 0 -3.735359710^{-4}
Standard deviation 1 0.9996158
test_that("Mean of z converges to 0 and standard deviation converges to 1", {
  expect_equivalent(
    round(
      x = mean_z,
      digits = 0
    ),
    0
  )
  expect_equivalent(
    round(
      x = sd_z,
      digits = 0
    ),
    1
  )
})
test_that("Mean of x converges to mu and standard deviation converges to sigma", {
  expect_equivalent(
    round(
      x = mean_x,
      digits = 0
    ),
    mu
  )
  expect_equivalent(
    round(
      x = sd_x,
      digits = 0
    ),
    sigma
  )
})