## Copyright (C) 1995, 1996, 1997  Kurt Hornik
## 
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
## 
## This program is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
## General Public License for more details. 
## 
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## usage:  [pval, z] = z_test (x, m, v [, alt])
##
## Perform a Z-test of the null hypothesis mean(x) == m for a sample x 
## from a normal distribution with unknown mean and known variance v. 
## Under the null, the test statistic z follows a standard normal
## distribution.
##
## With the optional argument string alt, the alternative of interest
## can be selected.  
## If alt is "!=" or "<>", the null is tested against the two-sided
## alternative mean(x) != m.
## If alt is ">", the one-sided alternative mean(x) > m is considered, 
## similarly for "<".  
## The default is the two-sided case.
##
## pval is the p-value of the test.
##  
## If no output argument is given, the p-value of the test is displayed
## along with some information. 

## Author:  KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description:  Test for mean of a normal sample with known variance

function [pval, z] = z_test (x, m, v, alt)
  
  if ((nargin < 3) || (nargin > 4))
    usage ("[pval, z] = z_test (x, m, v [, alt])");
  endif
    
  if (! is_vector (x))
    error ("z_test:  x must be a vector.");
  endif
  if (! is_scalar (m))
    error ("z_test:  m must be a scalar.");
  endif
  if (! (is_scalar (v) && (v > 0)))
    error ("z_test:  v must be a positive scalar.");
  endif
  
  n = length (x);
  z = sqrt (n/v) * (sum (x) / n - m);
  cdf = stdnormal_cdf (z);
  
  if (nargin == 3)
    alt = "!=";
  endif

  if (! isstr (alt))
    error ("z_test:  alt must be a string");
  elseif (strcmp (alt, "!=") || strcmp (alt, "<>"))
    pval = 2 * min (cdf, 1 - cdf);
  elseif (strcmp (alt, ">"))
    pval = 1 - cdf;
  elseif (strcmp (alt, "<"))
    pval = cdf;
  else
    error (sprintf ("z_test:  option %s not recognized", alt));
  endif
  
  if (nargout == 0)
    s = strcat ("Z-test of mean(x) == %g against mean(x) %s %g,\n",
	      	"with known var(x) == %g:\n",
	      	"  pval = %g\n");
    printf (s, m, alt, m, v, pval);
  endif

endfunction
