#------------------------------------------------------------------#
#EXAMPLE 1
#Sample size determination for estimating the population mean
# Population size not known
#sampling error
E <- 5
#prelimary estimate of sigma
sigma_est <- 25
#97.5th percentile of the standard normal distribution
z025 <- qnorm(.975)
z025
#sample size
n <- ((z025*sigma_est)/E)^2
n

# Population size known
#sampling error
E <- 5
#prelimary estimate of sigma
sigma_est <- 25
#population size
N <- 500
#97.5th percentile of the standard normal distribution
z025 <- qnorm(.975)
z025
#sample size
num <- N*(z025*sigma_est)^2
dem <- ((N-1)*(E^2))+(z025*sigma_est)^2
n <- num/dem
n

#-------------------------------------------------------------------#
#EXAMPLE 2
#Sample size determination for estimating the population proportion
# Population size not known 
#sampling error
E <- 0.01
#prelimary estimate of pi
pi_est <- 0.5
#97.5th percentile of the standard normal distribution
z025 <- qnorm(.975)
z025
#sample size
n <- (z025*(sqrt(pi_est*(1-pi_est)))/E)^2
n

# Population size known
#sampling error
E <- 0.01
#prelimary estimate of pi
pi_est <- 0.5
#population size
N <- 12350
#97.5th percentile of the standard normal distribution
z025 <- qnorm(.975)
z025
#sample size
n0 <- (z025*(sqrt(pi_est*(1-pi_est)))/E)^2
n0
n <- n0/(1+(n0-1)/N)
n

#-------------------------------------------------------------------#
#EXAMPLE 3
#Sample size determination for estimating the population variance
#sampling error  
E <- 0.1
#97.5th percentile of the standard normal distribution
z025 <- qnorm(.975)
z025
#sample size
n <- (0.5*(z025/E)^2) +1
n

#--------------------------------------------------------------------#
#EXAMPLE 4
#Sample size determination for estimating the population proportion
#sampling error
E <- 0.04
#prelimary estimate of pi
pi_est <- 0.5
#97.5th percentile of the standard normal distribution
z025 <- qnorm(.975)
z025
#sample size
n <- (z025*(sqrt(pi_est*(1-pi_est)))/E)^2
n

#Given the sample size obtain the sampling error  
#budget
budget <- 2400
#cost
cost <- 10
#sample size
n <- budget/cost
n
#97.5th percentile of the standard normal distribution
z025 <- qnorm(.975)
z025
#sampling error
E <- z025 * sqrt((pi_est*(1-pi_est))/n)
E

#--------------------------------------------------------------------#