# Examples on Construction CI's.
# Todo luego de signo de numero es un comentario

# Alzheimer example.
# n = 61
# The runif function generates n uniformly distributed random numbers 
# between min and max. The round function redondea. Note que el la
# siguiente linea es como una composicion de funciones, recuerda MECU!
n = round(runif(1,min=50,max=80))
Xbar = 48
sigma = 14
C = 0.95
pr = C + 0.025 # C + lower_tail_area
z = qnorm(pr,mean=0,sd=1,lower.tail=TRUE)
ME = z*sigma/sqrt(n)
lb = Xbar - ME
ub = Xbar + ME
cat("For Alzheimer example:\n Critical z =",z) # to display on screen
cat(". CI of level",C,"is [",lb,ub,"]\n")
cat ("The sample size is",n,".\n\n")

# Rents Example
# X = c(650,600,505,450,550,515,495,650,395,620)
# n = length(X)
n = 10
# The runif function generates n uniformly distributed random numbers 
# between min and max.
X = runif(n,min=395,max=650)
Xbar = mean(X)
s = sd(X)
C = 0.95
pr = C + 0.025
t = qt(pr,df=n-1) 
SE = s/sqrt(n)
ME = t*SE
lb = Xbar - ME
ub = Xbar + ME
cat("For Rents example:\n Critical t =",t)
cat(". CI of level",C,"is [",lb,ub,"]\n")
cat("Data is:\n",X,"\n\n")

# Example Periodicos
n = 200
X = 35
C = 0.90
phat = X/n
SE = sqrt((phat*(1-phat))/n)
z = qnorm(C+0.05,mean=0,sd=1)
ME = z*SE
lb = phat - ME
ub = phat + ME
cat("For Periodicos example:\n Critical t =",t)
cat(". CI of level",C,"is [",lb,ub,"]\n")