---
title: "Session 11 — Sampling distribution"
author: "Prof. Dae-Jin Lee (daelee@faculty.ie.edu)"
date: "Fall 2026"
output:
  html_document:
    toc: true
    theme: flatly
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
library(tidyverse)
```

```{r}
survey <- read_csv("data/survey_attitudes.csv")
x <- survey$support_international_cooperation

set.seed(11)
sample_means <- replicate(1000, mean(sample(x, size = 40, replace = TRUE)))

c(mean_of_means = mean(sample_means), se_approx = sd(sample_means))

tibble(sample_mean = sample_means) |>
  ggplot(aes(x = sample_mean)) +
  geom_histogram(bins = 30) +
  labs(
    title = "Sampling distribution of the mean (n = 40)",
    x = "Sample mean",
    y = "Frequency"
  )
```

**Interpret:** `sd(sample_means)` approximates the standard error of the mean for $n=40$.