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## Copyright (C) 1995-2013 Kurt Hornik
##
## This file is part of Octave.
##
## Octave 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 3 of the License, or (at
## your option) any later version.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{pval}, @var{z}] =} z_test (@var{x}, @var{m}, @var{v}, @var{alt})
## Perform a Z-test of the null hypothesis @code{mean (@var{x}) ==
## @var{m}} for a sample @var{x} from a normal distribution with unknown
## mean and known variance @var{v}. Under the null, the test statistic
## @var{z} follows a standard normal distribution.
##
## With the optional argument string @var{alt}, the alternative of
## interest can be selected. If @var{alt} is @qcode{"!="} or
## @qcode{"<>"}, the null is tested against the two-sided alternative
## @code{mean (@var{x}) != @var{m}}. If @var{alt} is @qcode{">"}, the
## one-sided alternative @code{mean (@var{x}) > @var{m}} is considered.
## Similarly for @qcode{"<"}, the one-sided alternative @code{mean
## (@var{x}) < @var{m}} is considered. The default is the two-sided
## case.
##
## The p-value of the test is returned in @var{pval}.
##
## If no output argument is given, the p-value of the test is displayed
## along with some information.
## @end deftypefn
## Author: KH <Kurt.Hornik@wu-wien.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))
print_usage ();
endif
if (! isvector (x))
error ("z_test: X must be a vector");
endif
if (! isscalar (m))
error ("z_test: M must be a scalar");
endif
if (! (isscalar (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 (! ischar (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 ("z_test: option %s not recognized", alt);
endif
if (nargout == 0)
s = ["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
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