#Example 1
# Testing hypothesis about two  population variances 

#Set working directory
setwd("~/Dropbox/ISI SCB/Data sets")

# read in csv file
sh <-read.csv("sheets.csv", TRUE)

#1:Machine 1
#2:Machine 2
#assign the list of thickness measures to the variable x 
#for Machine 1
x <- sh$Thickness[sh$Machine==1]

#assign the list of thickness measures  to the variable y 
#for Machine 2
y <- sh$Thickness[sh$Machine==2]

#sample variances 
cbind(var(x), var(y))

# test for equality of variances
var.test(x,y) 


#check for outliers
boxplot(x,y)

#assess normality assumptions of x and y
qqnorm(x, ylab = "x Sample Quantiles")
shapiro.test(x)
qqnorm(y, ylab = "y Sample Quantiles")
shapiro.test(y)

# test for equality of variances with 99% C.I.
var.test(x,y,conf.level = 0.99)