---
title: "Sample proportions"
author: "Milica Cudina"
date: "`r Sys.Date()`"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
## Setting up the populations
First, we set up some proportions in the population of who would be *for* solar panels and who would be *against*.
```{r}
n.pop=3*10^8
opinions=c(rep("for", 0.88*n.pop),rep("against", 0.12*n.pop))
```
## Drawing a sample
Then, we draw a sample of size $1000$ without replacement.  
```{r}
sample.size=1000
srs=sample(opinions, size = sample.size)
#srs
```
## Finding the point estimate
Now, we find the sample proportion of the number of supporters. 
```{r}
p.hat=mean(srs=="for")
p.hat
```
## What if we repeat this procedure, say, 1000 times?
Finally, let's see what the shape of the sampling distribution of the sample proportion is. 

```{r}
p.hat.vector=numeric()
for (i in 1:1000){
    srs=sample(opinions, size = sample.size)
    p.hat=mean(srs=="for")
    p.hat.vector=append(p.hat.vector,p.hat)  
}
hist(p.hat.vector, col="orange")
```