server.R

library(shiny)
cnorm <- function(n){
  val <- rnorm(n)
  uval <- runif(n)
  flag <- (uval <= 1 - 0.1)
  val[!flag] <- 10 * val[!flag]
  val
}
shinyServer(function(input, output){
  data <- reactive(function(){
    Distribution <- switch(input$Distribution,
                           Normal = rnorm,
                           Uniform = runif,
                           Lognormal = rlnorm,
                           Exponential = rexp,
                           "Contaminated Normal" = cnorm,
                           rnorm
                           )
    Distribution(input$sam_size*2000)
    
    
  })
  
  output$plot <- reactivePlot(function(){
    Distribution <- input$Distribution
    sam_size <- input$sam_size
    temp <- matrix(data(), ncol=2000)
    xbars <- colMeans(temp)
    SD <- sd(xbars)
    MEAN <- mean(xbars)
    ylimits <- range(hist(xbars, br=25)$density, density(xbars)$y)
    hist(xbars, br=25, ylim=ylimits,
         main=paste("Sampling Distribution of the Mean\nBased on a", Distribution,
                             "Distribution with n =", sam_size), freq=FALSE)
    lines(density(xbars))
    curve(dnorm(x, mean=MEAN, sd=SD), add=T, lty=3)
    })
  
})

ui.R

library(shiny)

# Define UI for application that plots random distributions 
shinyUI(pageWithSidebar(
  
  # Application title
  headerPanel("Central Limit Theorem"),
  
  # Sidebar with a slider input for number of observations
  sidebarPanel(
    selectInput("Distribution", "Distribution:",
                list("Normal", "Lognormal", "Contaminated Normal", "Exponential")),
    br(),
    sliderInput("sam_size", 
                "Sample size:", 
                min = 5, 
                max = 500, 
                value = 5)
  
  ),
  mainPanel(
      tabPanel("Plot", plotOutput("plot")
      )
    )
))