clear all 
close all 
mu = 75; % Population mean
sigma = 2; % Population standard deviation
n = 20; % Sample size
e = normrnd(mu,sigma,n,1); % Random sample from population


xbar = mean(e) % Sample mean
s = std(e) % Sample standard deviation


gamma = 0.95 % P(-A< T < A) =0.95
t = tinv((1+gamma)/2,n-1) %correspond to  P(T <= A) =(1+gamma)/2

lb = xbar-t*s/sqrt(n)
ub = xbar+t*s/sqrt(n)


figure;
subplot(131),plot(e,'o')
hold on 
subplot(131),plot(zeros(1,n)+ub,'r');
subplot(131),plot(zeros(1,n)+xbar,'k');
subplot(131),plot(zeros(1,n)+lb,'g');





mu = 75; % Population mean
sigma = 2; % Population standard deviation
n = 10; % Sample size
e = normrnd(mu,sigma,n,1); % Random sample from population



xbar = mean(e) % Sample mean
s = std(e) % Sample standard deviation

gamma = 0.95 % P(-A< T < A) =0.95
t = tinv((1+gamma)/2,n-1) %correspond to  P(T <= A) =(1+gamma)/2


lb = xbar-t*s/sqrt(n)
ub = xbar+t*s/sqrt(n)




subplot(132),plot(e,'o')
hold on 
subplot(132),plot(zeros(1,n)+ub,'r');
subplot(132),plot(zeros(1,n)+xbar,'k');
subplot(132),plot(zeros(1,n)+lb,'g');


mu = 75; % Population mean
sigma = 2; % Population standard deviation
n = 5; % Sample size
e = normrnd(mu,sigma,n,1); % Random sample from population



xbar = mean(e) % Sample mean
s = std(e) % Sample standard deviation

gamma = 0.95 % P(-A< T < A) =0.95
t = tinv((1+gamma)/2,n-1) %correspond to  P(T <= A) =(1+gamma)/2


lb = xbar-t*s/sqrt(n)
ub = xbar+t*s/sqrt(n)




subplot(133),plot(e,'o')
hold on 
subplot(133),plot(zeros(1,n)+ub,'r');
subplot(133),plot(zeros(1,n)+xbar,'k');
subplot(133),plot(zeros(1,n)+lb,'g');