做模拟的时候你知道真实的参数值，然后比如说你模拟了1000次，算了1000个置信区间，看一下其中多少个包含了真实的参数值就行了。

suppose the random variables x1,x2,...,xn are a random sample from a N(mu, sigma^2) distribution.

R command:

sample mean of x : mean(x)
standard deviation of x : sd(x)
the 97.5th percentile of the t-distribution with 15 degrees of freedom : qt(0.975, 15)

so, the R script is:

inORnot <- function(alpha, n, mu, sigma) {

  x = rnorm(n, mean = mu, sd = sigma)

  L = mean(x) - qt(1 - alpha / 2, n - 1)*sd(x)/sqrt(n)
  U = mean(x) + qt(1 - alpha / 2, n - 1)*sd(x)/sqrt(n)

  return(L <= mu & U >= mu)

}

tau <- function(alpha, S, n) {

  cum = 0
  for (i in 1:S) cum = cum + inORnot(alpha, n, mu = 0, sigma = 1)
  return(cum / S)

}

> tau(alpha = 0.05, S = 1000, n = 100)
[1] 0.957

非常感谢您的回复，谢谢了！！