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- > 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
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