#Relació entre la distribució de la mitjana mostral 
#i la població a mesura que incrementa la mida mostral

mu0 <- 2; 
muA <- 4;
sigma <- 1;
alfa<-0.05



# Generació del grŕfic


eix <- c(mu0 - 3 * sigma, muA + 3 * sigma)
x <- seq(eix[1], eix[2], length = 1001)
y <- 1.25*dnorm(x, mu0, sigma)
plot(x, y, type='n', xlab = '', ylab = expression(italic(Densitat)), lwd=2, main='Error Tipus I vs. Error Tipus II')
abline(h = 0)
x1 <- x[x >= qnorm(1-alfa,mu0,sigma)] ; y1 <- dnorm(x1, mu0, sigma)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'grey10', border='grey10', density=90, angle=-45)
x1 <- x[x <= qnorm(1-alfa,mu0,sigma)] ; y1 <- dnorm(x1, muA, sigma)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'grey40', border='grey40', density=20, angle=45)
x1 <- x[x <= qnorm(1-alfa,mu0,sigma)] ; y1 <- dnorm(x1, mu0, sigma)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, border='grey10', lty=2,lwd=2)
x1 <- x[x >= qnorm(1-alfa,mu0,sigma)] ; y1 <- dnorm(x1, muA, sigma)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, border='grey40', lty=2, lwd=2)

#Afegim Text
text(mu0, 1.10*dnorm(mu0,mu0,sigma), expression(italic(mu[0])), cex=1.5, )
text(muA, 1.10*dnorm(muA,muA,sigma), expression(italic(mu[1])), cex=1.5)

text(mu0-2.5*sigma, 0.55*dnorm(mu0,mu0,sigma), expression(italic(1-alpha)), col='grey10', cex=1.5)
text(mu0-2.5*sigma, 0.5*dnorm(mu0,mu0,sigma), 1-alfa, col='grey10', cex=1.5)

text(mu0-2.5*sigma, 0.25*dnorm(mu0,mu0,sigma), expression(italic(beta)), col='grey40', cex=1.5)
text(mu0-2.5*sigma, 0.2*dnorm(mu0,mu0,sigma), beta, col='grey40', cex=1.5)

text(muA+2.5*sigma, 0.55*dnorm(mu0,mu0,sigma), expression(italic(1-beta)), col='grey40', cex=1.5)
text(muA+2.5*sigma, 0.5*dnorm(mu0,mu0,sigma), 1-beta, col='grey40', cex=1.5)

text(muA+2.5*sigma, 0.25*dnorm(mu0,mu0,sigma), expression(italic(alpha)), col='grey10', cex=1.5)
text(muA+2.5*sigma, 0.2*dnorm(mu0,mu0,sigma), alfa, col='grey10', cex=1.5)
mtext(side=1, line=-3, cex=0.75, outer=T, adj=1, "Script creat per Jordi López-Tamayo  ")