%
% epage 241
% 
% bootstrap confinence interval of the mean
% 
% 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 forearm; 

% get the standard percentile interval for the sample second moment (using the bootstrap): 
fn = @mean;
B = 1500; 
alpha = 0.1; 
qhat = bootstrp_sci( B, fn, forearm, alpha ); 
fprintf( 'the mean for the forearm data = %10.5f:\n', mean(forearm) ); 
fprintf( 'the empirical bootstrap computed estimates percentile interval are given by:\n' );
fprintf( '%10.5f', qhat ); fprintf('\n'); 

% get the standard percentile interval for the sample second moment
%  (using the the known distribution) of the sample mean:
mu0     = mean(forearm);    % <- assume this is the POPULATION mean
nd      = length(forearm);  % <- the number of samples 
std0    = std(forearm);     % <- assume this is the POPULATION standard deviation
meanStd = std0/sqrt(nd);    % <- the known standard deviation of the statistic (the mean)
qhat = norminv( [ 0.5*alpha, 1-0.5*alpha ], mu0, meanStd ); 
fprintf( 'the theoretical computed estimates percentile interval are given by:\n' );
fprintf( '%10.5f', qhat ); fprintf('\n');