```
#create an app that plots the sample size agaist margin of error given sample size and standard deviation
#define UI
ui <- fluidPage(
h1("Central Limit Theorem - CLT"), #heading
titlePanel("Margin of error"), #add the label as an argument
sidebarLayout(
sidebarPanel("Input your standard deviation",
numericInput(inputId = "stanDev", label = "standard deviation", value = 10),
numericInput(inputId = "smpl", "sample size", value = 16),
),
mainPanel("Sample size against Margin of error!",
textOutput("plot"))
))
server <- function(input, output) {
calc_sem<-(1.96 * input$stanDev/sqrt(input$smpl))
population <- ceiling(runif(2700, 150, 250)) #model the population using 2700 uniformly drawn integers(assumption we can use any)
sample_sem<- for (i in 1:input$smpl) { #Calculate SEM for samples ranging in size from 1 to smpl entered
samp[[i]]<-sample(population, i)
sem[[i]]<-calc_sem(samp[[i]])}
#creating a DF and adding a col for the sample size
sem_df<-data.frame(sem)
sem_df["size"]<-c(1:input$smpl)
# code for the plot
output$plot <-renderPlot({
plot(sample_sem,aes(x = size, y = sem))+geom_line()+xlab("Sample Size")+ylab("Standard Error of the Mean")
}
}
#run the app
shinyApp(ui, server)
```

I recommend that you study the basics of shiny reactivity from

Chapter 3 Basic reactivity | Mastering Shiny (mastering-shiny.org)

in particular focus on section 3.3.4 Reactive expressions

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