mu <- 10
sigma <- 2
n <- 100
nreps <- 10000
pv <- rep(NA, nreps)
inout <- rep(NA, nreps)
inout_1 <- rep(NA, nreps)
inout_2 <- rep(NA, nreps)
inout_3 <- rep(NA, nreps)


for(i in 1:nreps){
  #print(i)
  set.seed(i)
  x <- rnorm(n, mu, sigma)
  pv[i] <- t.test(x, mu = 10)$p.value
  lower <- t.test(x, mu = 10)$conf.int[1]
  upper <- t.test(x, mu = 10)$conf.int[2]
  inout[i] <- ifelse(10 >= lower & 10 <= upper,1,0)
  inout_1[i] <- ifelse(9.5 <= lower,1,0)
  
    }
#inout
mean(1-inout)
#inout_1
mean(1-inout_1)

for(i in 1:nreps){
  #print(i)
  set.seed(i)
  x <- rnorm(n, mu, sigma)
  pv[i] <- t.test(x, mu = 10)$p.value
  lower <- t.test(x, mu = 10)$conf.int[1]
  upper <- t.test(x, mu = 10)$conf.int[2]
  inout[i] <- ifelse(10 >= lower & 10 <= upper,1,0)
  inout_2[i] <- ifelse(9.3 <= lower,1,0)

   }
#inout
mean(1-inout)
#inout_2
mean(1-inout_2)


for(i in 1:nreps){
  #print(i)
  set.seed(i)
  x <- rnorm(n, mu, sigma)
  pv[i] <- t.test(x, mu = 10)$p.value
  lower <- t.test(x, mu = 10)$conf.int[1]
  upper <- t.test(x, mu = 10)$conf.int[2]
  inout[i] <- ifelse(10 >= lower & 10 <= upper,1,0)
  inout_3[i] <- ifelse(9.2 <= lower,1,0)
  
}
#inout
mean(1-inout)
#inout_3
mean(1-inout_3)