# conf.int()

## Demonstration of Confidence Intervals

### Yihui Xie & Lijia Yu / 2017-04-04

This function gives a demonstration of the concept of confidence intervals in mathematical statistics.

Keep on drawing samples from the Normal distribution N(0, 1), computing the intervals based on a given confidence level and plotting them as segments in a graph. In the end, we may check the coverage rate against the given confidence level.

Intervals that cover the true parameter are denoted in color `cl[2]`

,
otherwise in color `cl[1]`

. Each time we draw a sample, we can compute
the corresponding confidence interval. As the process of drawing samples goes
on, there will be a legend indicating the numbers of the two kinds of
intervals respectively and the coverage rate is also denoted in the top-left
of the plot.

The argument `nmax`

in `ani.options`

controls the maximum
times of drawing samples.

```
library(animation)
ani.options(interval = 0.1, nmax = 100)
## 90% interval
conf.int(0.9, main = "Demonstration of Confidence Intervals")
```

plot of chunk demo-a

This animation shows the concept of the confidence interval which depends on the observations: if the samples change, the interval changes too. At last we can see that the coverage rate will be approximate to the confidence level.