## Problem A

setwd("C:/local/classes/M483")
data <- read.csv('R-iris.txt', header = T)
 names(data)
 attach(data)
 
 seto <- Setosa
 vers <- Versicolor
 mean(seto)
 sd(seto)

 n <- length(seto)
 qqnorm(seto)       # the plot looks very normal

 qt(0.975, n - 1)

  me <- qt(0.975, n - 1)*sd(seto)/sqrt(n)
  c(5.006 - me, 5.006 + me)       ## part a
  (inv <- c(qchisq(0.05,n-1), qchisq(0.95,n-1)))  ## part b
  (sigma.ci <- sd(seto)*sqrt((n-1)/inv) )
 
  (ci.ratio <- sd(seto)/sd(vers)*sqrt(c(qf(0.05, 49, 49), qf(0.95, 49, 49))) )