# Demonstration of the concept of confidence intervals

### Description

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

### Usage

1 |

### Arguments

`level` |
the confidence level |

`size` |
the sample size for drawing samples from N(0, 1) |

`cl` |
two different colors to annotate whether the confidence intervals
cover the true mean ( |

`...` |
other arguments passed to |

### Details

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.

### Value

A list containing

`level ` |
confidence level |

`size ` |
sample size |

`CI` |
a matrix of confidence intervals for each sample |

`CR` |
coverage rate |

### Author(s)

Yihui Xie

### References

George Casella and Roger L. Berger. *Statistical Inference*.
Duxbury Press, 2th edition, 2001.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
oopt = ani.options(interval = 0.1, nmax = ifelse(interactive(), 100, 2))
## 90% interval
conf.int(0.9, main = "Demonstration of Confidence Intervals")
## save the animation in HTML pages
saveHTML({
ani.options(interval = 0.15, nmax = ifelse(interactive(), 100, 10))
par(mar = c(3, 3, 1, 0.5), mgp = c(1.5, 0.5, 0), tcl = -0.3)
conf.int()
}, img.name = "conf.int", htmlfile = "conf.int.html", ani.height = 400,
ani.width = 600, title = "Demonstration of Confidence Intervals",
description = c("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."))
ani.options(oopt)
``` |