t.1.sample <- function(xbar,mu_0,s,n,alpha=0.05,tails=2)
{
  ## compute t statistic
  df <- n-1
  t <- sqrt(n)*(xbar - mu_0)/s
  # compute critical value
  if(tails == -1) p <- alpha
  if(tails == 1) p <- 1-alpha
  if(tails == 2) p <- c(alpha/2,1 - alpha/2)
  crit <- qt(p,df)
# create a list of named quantities and return it
  res <- list(t.statistic = t, df = df, alpha = alpha, 
              critical.t.values = crit)
  return(res)
}

t.1.sample.ci <- function(xbar,s,n,conf=.95){
  se.xbar <- s/sqrt(n)
  df <- n-1
  alpha <- 1 - conf
  p <- 1 - alpha/2
  t.crit <- qt(p,df)
  diff <- t.crit * se.xbar
  lower <- xbar - diff
  upper <- xbar + diff
  res <- list(lower.limit=lower,upper.limit=upper,confidence.level = conf)
  return(res)
}