bsp_4_3.m

% Beispiel für Kap 4.3
%% erzeuge Beispielwerte für Kap. 4-3
% Quantile der Standard-Normalverteilung
alpha = [10, 5, 2, 1, 0.5, 0.1]/100;
x_al = norminv(1-alpha/2);

% Beispiel Füllmengen
mu = 0.72;
sigma = 0.03;
n = 20;
alpha = 0.05;
rng('default');  % For reproducibility
xi = normrnd(mu, sigma, 1, n);
xq = mean(xi)
z = norminv(1 - alpha/2)
gu = xq - sigma*z/sqrt(n)
go = xq + sigma*z/sqrt(n)

s = std(xi)
s2 = s^2
t = tinv(1 - alpha/2, n-1)
gu = xq - s*t/sqrt(n)
go = xq + s*t/sqrt(n)

chiu = chi2inv(1 - alpha/2, n-1)
chio = chi2inv(alpha/2, n-1)
gu = (n-1)*s2/chiu
go = (n-1)*s2/chio
sigu = sqrt(gu)
sigo = sqrt(go)


%% Beispiel Würfel
n = 30;
rng(4);  % For reproducibility
xi = floor(6*rand(1,n)) + 1;
alpha = 0.05;
y = sum(xi == 6)
z = norminv(1 - alpha/2)
xq = y/n
gu = (xq + z^2/(2*n) - (z/sqrt(n))*sqrt(xq*(1-xq) + z^2/(4*n)))/(1+z^2/n)
go = (xq + z^2/(2*n) + (z/sqrt(n))*sqrt(xq*(1-xq) + z^2/(4*n)))/(1+z^2/n)