%
% example 219 
%
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; 
clc; 

addpath('../../Code/CSTool');
load mcdata;   % 

n = length(mcdata); 
% assume we know the population sigma: 
sigma = 7.8; 
% this implies we know the standard deviation of the sample mean: 
sigxbar = sigma/sqrt(n);
% get the observed value of the test statistic: 
Tobs = (mean(mcdata)-454)/sigxbar; 
disp( 'our observed test statistic is...' ); 
Tobs 

% perform a monte-carlo simulation (where we generate a random sample under H_0) 
% used to determine the distribution of our test statistic:
M  = 1000; 
Tm = zeros(1,M); 
for i=1:M,
  xs = sigma*randn(1,n) + 454; 
  Tm(i) = (mean(xs)-454)/sigxbar;
end

% pick a significance level:
alpha = 0.1; 
% find the \hat{q}_{\alpha/2} and \hat{q}_{1-\alpha/2} quantiles for our statistic T (under H_0): 
%qhat = sample_quantiles_linInterp(Tm,[0.5*alpha, 1-0.5*alpha]);
disp( 'the qhat quantiles are...' ); 
qhat = csquantiles(Tm,[0.5*alpha, 1-0.5*alpha])