#Jordi López-Tamayo, Gener 2011
#Relació entre la distribució de la proporció mostral 
#i la mida mostral

phi <- 0.5 ; 
IInf <-0.45
ISup <-0.55
Text_I <-paste("[",IInf,",",ISup,"]")
# Generació del grŕfic
Text_I
par(mfrow=c(2,2), oma=c(0, 0, 4, 0))


nobs<-20
sigma_m <-sqrt(phi*(1-phi)/nobs); 
eix <- c(0,1)
x <- seq(eix[1], eix[2], length = 1001)
y <- dnorm(x, phi, sigma_m)
plot(x, y, type='l', xlab = expression(italic(n==20)), ylab = expression(italic(Densitat)))
abline(h = 0)
x1 <- x[x >= IInf &  x<= ISup] ; y1 <- dnorm(x1, phi, sigma_m)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'blue')
#Afegim Text
pr<-pnorm(ISup, phi, sigma_m)-pnorm(IInf, phi, sigma_m)
text(0.85, 0.85*dnorm(0.5,0.5,sigma_m), Text_I)
text(0.85, 0.75*dnorm(0.5,0.5,sigma_m), round(pr, digits=3))

nobs<-30
sigma_m <-sqrt(phi*(1-phi)/nobs); 
x <- seq(eix[1], eix[2], length = 1001)
y <- dnorm(x, phi, sigma_m)
plot(x, y, type='l', xlab = expression(italic(n==30)), ylab = expression(italic(Densitat)))
abline(h = 0)
x1 <- x[x >= IInf &  x<= ISup] ; y1 <- dnorm(x1, phi, sigma_m)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'blue')
pr<-pnorm(ISup, phi, sigma_m)-pnorm(IInf, phi, sigma_m)
text(0.85, 0.85*dnorm(0.5,0.5,sigma_m), Text_I)
text(0.85, 0.75*dnorm(0.5,0.5,sigma_m), round(pr, digits=3))

nobs<-50
sigma_m <-sqrt(phi*(1-phi)/nobs); 
x <- seq(eix[1], eix[2], length = 1001)
y <- dnorm(x, phi, sigma_m)
plot(x, y, type='l', xlab = expression(italic(n==50)), ylab = expression(italic(Densitat)))
abline(h = 0)
x1 <- x[x >= IInf &  x<= ISup] ; y1 <- dnorm(x1, phi, sigma_m)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'blue')
#Afegim Text
pr<-pnorm(ISup, phi, sigma_m)-pnorm(IInf, phi, sigma_m)
text(0.85, 0.85*dnorm(0.5,0.5,sigma_m), Text_I)
text(0.85, 0.75*dnorm(0.5,0.5,sigma_m), round(pr, digits=3))

nobs<-100
sigma_m <-sqrt(phi*(1-phi)/nobs); 
x <- seq(eix[1], eix[2], length = 1001)
y <- dnorm(x, phi, sigma_m)
plot(x, y, type='l', xlab = expression(italic(n==100)), ylab = expression(italic(Densitat)))
abline(h = 0)
x1 <- x[x >= IInf &  x<= ISup] ; y1 <- dnorm(x1, phi, sigma_m)
x2 <- c(x1[1],x1, x1[length(x1)], x1[1])
y2 <- c(0, y1, 0, 0)
polygon(x2, y2, col = 'blue')
#Afegim Text
pr<-pnorm(ISup, phi, sigma_m)-pnorm(IInf, phi, sigma_m)
text(0.85, 0.85*dnorm(0.5,0.5,sigma_m), Text_I)
text(0.85, 0.75*dnorm(0.5,0.5,sigma_m), round(pr, digits=3))

mtext(side=3, line=0, cex=1.5, outer=T,"Relació entre la proporció mostral i la mida mostral")
mtext(side=1, line=-2, cex=0.75, outer=T, adj=1, "Script creat per Jordi López-Tamayo")