This function gives a demonstration of the concept of confidence intervals in mathematical statistics.
conf.int(level = 0.95, size = 50, cl = c("red", "gray"), ...)the confidence level \((1 - \alpha)\), e.g. 0.95
the sample size for drawing samples from N(0, 1)
two different colors to annotate whether the confidence intervals
cover the true mean (cl[1]: no; cl[2]: yes)
other arguments passed to plot.default
A list containing
confidence level
sample size
a matrix of confidence intervals for each sample
coverage rate
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.
Examples at https://yihui.org/animation/example/conf-int/
George Casella and Roger L. Berger. Statistical Inference. Duxbury Press, 2th edition, 2001.