> a <- 0
> b <- 1
> mu <- (a+b)/2
> nsim <- 1e+5
> hits <- 0
> n <- 10
> for (i in 1:nsim) {
+   x <- runif(n, a, b)
+   ci <- confint(lm(x ~ 1))
+   if (ci[1] < mu & ci[2] > mu)
+     hits <- hits + 1
+ }
> hits/nsim
[1] 0.94738

> l1 <- l2 <- numeric(nsim)
> hits2 <- 0
> n <- 10
> pm <- c(-1,1)
> for (i in 1:nsim) {
+   x <- runif(n, a, b)
+   ci <- confint(lm(x ~ 1))
+   l1[i] <- ci[2]-ci[1]
+   ci2 <- (min(x)+max(x))/2 + pm*(max(x)-min(x))/2*(1/0.05^(1/(n-1))-1)
+   l2[i] <- ci2[2]-ci2[1]
+   if (ci[1] < mu & ci[2] > mu)
+     hits <- hits + 1
+   if (ci2[1] < mu & ci2[2] > mu)
+     hits2 <- hits2 + 1
+ }
> hits2/nsim
[1] 0.94917
> mean(l1)
[1] 0.407362
> mean(l2)
[1] 0.3230234