-```{r}
-est = .45
-sample_size = 50
-SE = sqrt(est*(1-est)/sample_size)
-
-conf_int = c(est - 1.96 * SE, est + 1.96 * SE)
-conf_int
-```
-
-What if we had the same result but had sampled 500 people?
-
-
-```{r}
-est = .45
-sample_size = 500
-SE = sqrt(est*(1-est)/sample_size)
-
-conf_int = c(est - 1.96 * SE, est + 1.96 * SE)
-conf_int
-```
-
-### Tabular Data
-
-The Iris dataset is composed of measurements of flower dimensions. It comes packaged with R and is often used in examples. Here we make a table of how often each species in the dataset has a sepal width greater than 3.
-
-```{r}
-
-table(iris$Species, iris$Sepal.Width > 3)
-
-```
-
-
-The chi-squared test is a test of how much the frequencies we see in a table differ from what we would expect if there was no difference between the groups.
-
-```{r}
-
-chisq.test(table(iris$Species, iris$Sepal.Width > 3))
-```
-
-The incredibly low p-value means that it is very unlikely that these came from the same distribution and that sepal width differs by species.
-
-
-
-## Using Simulation
-
-When the assumptions of Chi-squared tests aren't met, we can use simulation to approximate how likely a given result is.
-
-The book uses the example of a medical practitioner who has 3 complications out of 62 procedures, while the typical rate is 10%.
-
-The null hypothesis is that this practitioner's true rate is also 10%, so we're trying to figure out how rare it would be to have 3 or fewer complications, if the true rate is 10%.
-
-```{r}
-# We write a function that we are going to replicate
-simulation <- function(rate = .1, n = 62){
- # Draw n random numbers from a uniform distribution from 0 to 1
- draws = runif(n)
- # If rate = .4, on average, .4 of the draws will be less than .4
- # So, we consider those draws where the value is less than `rate` as complications
- complication_count = sum(draws < rate)
- # Then, we return the total count
- return(complication_count)
-}
-
-# The replicate function runs a function many times
-
-simulated_complications <- replicate(5000, simulation())
-
-```
-
-We can look at our simulated complications
-
-```{r}
-
-hist(simulated_complications)
-```
-
-And determine how many of them are as extreme or more extreme than the value we saw. This is the p-value.
-
-```{r}
-
-sum(simulated_complications <= 3)/length(simulated_complications)
-```
-