%Classifier comparison example

close all 
clear all 
mu = 79; % Population mean
sigma = 2; % Population standard deviation
n = 5; % Sample size
x = normrnd(mu,sigma,n,1); % Random sample from population

mu = 75.6; % Population mean
sigma = 2; % Population standard deviation
y = normrnd(mu,sigma,n,1);

xbar = mean(x);
ybar = mean(y);
sx = var(x);
sy = var(y);

%significance of test
alpha = 0.05;

t = tinv(1-alpha/2,n-1);
s = sqrt((sx+sy)/n);

fprintf('t=%.3f\n', t);
fprintf('s=%.3f\n', s);
fprintf('xbar-ybar = %f\n', xbar-ybar); 
lb = -t*sqrt(s/n);
ub = t*sqrt(s/n);

fprintf('IC = (%.3f,%.3f)\n', lb,ub);



if (abs(xbar-ybar)/sqrt(s/n)>= t)
    fprintf('H_0 rejected\n')
else
    fprintf('H_0 accepted\n')
end



figure;
subplot(121),plot(x,'o');
hold on;
plot(zeros(1,20)+xbar,'k');
subplot(122),plot(y,'or');
hold on;
plot(zeros(1,20)+ybar,'k');