# Roger Palay copyright 2016-01-31
# Saline, MI 48176
#
hypoth_test_unknown <- function(
  H0_mu,  H1_type=0, sig_level=0.05,
  samp_size, samp_mean, samp_sd)
{ # perform a hypothesis test for the mean=H0_mu
  # when we do not know sigma and the alternative hypothesis is
  #      !=  if H1_type==0
  #      <   if H1_type < 0
  #      >   if H1_type > 0
  # Do the test at sig_level significance, for a 
  # sample of size samp_size that yields a sample
  # mean = samp_mean and a sample standard deviation = samp_sd
  s_x <- samp_sd/sqrt(samp_size)
  if( H1_type == 0)
  { t <- abs( qt(sig_level/2,samp_size-1))}
  else
  { t <- abs( qt(sig_level,samp_size-1))}
  to_be_extreme <- t*s_x
  decision <- "Reject"
  if( H1_type < 0 )
    { crit_low <- H0_mu - to_be_extreme
      crit_high = "n.a."
      if( samp_mean > crit_low)
        { decision <- "do not reject"}
      attained <- pt( (samp_mean-H0_mu)/s_x, samp_size-1)
      alt <- paste("mu < ", H0_mu)
    }
  else if ( H1_type == 0)
  { crit_low <- H0_mu - to_be_extreme 
    crit_high <- H0_mu + to_be_extreme
    if( (crit_low < samp_mean) & (samp_mean < crit_high) )
        { decision <- "do not reject"}

    if( samp_mean < H0_mu )
      { attained <- 2*pt((samp_mean-H0_mu)/s_x,samp_size-1)}
    else
      { attained <- 2*pt((samp_mean-H0_mu)/s_x, samp_size-1,
                     lower.tail=FALSE)
      }
    alt <- paste( "mu != ", H0_mu)
  }
  else
    { crit_low <- "n.a."
      crit_high <- H0_mu + to_be_extreme
      if( samp_mean < crit_high)
        { decision <- "do not reject"}
      attained <- pt((samp_mean-H0_mu)/s_x, samp_size-1,
                 lower.tail=FALSE)
      alt <- paste("mu > ",H0_mu)
    }
  ts <- (samp_mean - H0_mu)/(samp_sd/sqrt(samp_size))
  result <- c(H0_mu, alt, s_x, samp_size, sig_level, t,
              samp_mean, samp_sd, ts, to_be_extreme,
              crit_low, crit_high, attained, decision)
  names(result) <- c("H0_mu", "H1:", "std. error", "n",
                     "sig level", "t"  ,"samp mean",  
                     "samp stdev", "test stat", "how far",
                     "critical low", "critical high",
                     "attained", "decision")
  return( result)
}