# R-program for Supplementary Exercises 6.13 and 6.14 of IPS7e
# R does not have a built-in function for this model because it is unrealistic in practice
# - this solution shows 3 different approaches to do the analysis anyway...

corn <- read.csv("r:/Chapter 6/ex06_013.csv")

# method 1: manual calculation using formulae
mean <- mean(corn$Yield)
n <- length(corn$Yield)
sd <- 10
se <- sd/sqrt(n)
# 90% CI:
lower <- mean-qnorm(0.95)*se; upper <- mean+qnorm(0.95)*se; as.vector(c(lower,upper))
# 95% CI:
lower <- mean-qnorm(0.975)*se; upper <- mean+qnorm(0.975)*se; as.vector(c(lower,upper))
# 99% CI:
lower <- mean-qnorm(0.995)*se; upper <- mean+qnorm(0.995)*se; as.vector(c(lower,upper))
# 95% CI for hypothetical sample of size 50 with mean 123.8
lower <- 123.8-qnorm(0.975)*sd/sqrt(50); upper <- 123.8+qnorm(0.975)*sd/sqrt(50)
as.vector(c(lower,upper))

# method 2: write a function to do the calculation
# based on: http://www.r-bloggers.com/one-sample-z-test/
z.ci = function(a, sd, conf.level=0.95){
   lower = mean(a) - qnorm(1-(1-conf.level)/2)*sd/sqrt(length(a))
   upper = mean(a) + qnorm(1-(1-conf.level)/2)*sd/sqrt(length(a))
   return(as.vector(c(lower,upper)))
}
z.ci(corn$Yield, sd=10, conf.level=0.90)
z.ci(corn$Yield, sd=10, conf.level=0.95)
z.ci(corn$Yield, sd=10, conf.level=0.99)
z.ci(c(123.8), sd=10/sqrt(50), conf.level=0.95)
# last calculation forges a sample size of 50 by dividing the sd by sqrt(50)

# method 3: using add-on library TeachingDemos
# note: it is not always a good idea to just use some add-on library...
# ignore the z-test and use only the CI
library(TeachingDemos)
z.test(corn$Yield, sd=10, conf.level=0.90)
z.test(corn$Yield, sd=10, conf.level=0.95)
z.test(corn$Yield, sd=10, conf.level=0.99)
z.test(c(123.80), sd=10/sqrt(50), conf.level=0.95)
# same trick as above for last calculation