# simulation study of CI coverage when assumptions of t-test are violated
# 

M <- 10000
ctr <- 0
n1 <- 20
n2 <- 5    # unequal sample sizes
tstar <- qt(0.975, df = n1+n2-2)

  for (mc in 1:M){
    Y1 <- rexp(n1, rate = 1/sqrt(2)) - sqrt(2)
    Y2 <- runif(n2,-0.5,0.5)       # rt(n2, df=4)    
    sp <- sqrt(var(Y1)*(n1-1) + var(Y2)*(n2-1)) / sqrt(n1+n2-2)
    half <- tstar*sp*sqrt(1/n1 + 1/n2)
    if (abs(mean(Y2) - mean(Y1)) > half){
        ctr <- ctr + 1 
    }  
  }

 print( paste("failure rate of supposedly 95% C.I.", ctr/M) )