#Example 2
# Testing hypothesis about two related population means
#paired samples

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

# read in csv file
sk <-read.csv("skills.csv", TRUE)

#assign the list of scores to the variable x 
#for "Post-training' test
x <- sk$After.Score

#assign the list of reading scores to the variable y 
#for "Pre-training' test
y <- sk$Before.Score


#D= Post-training - Pre-training 
#H0: muD = 0 , H1: muD > 0 
#t-test
t.test(x,y, alternative="greater", paired = TRUE)



# this will enable us to get a 95% two-sided confidence iterval
#H0: muD = 0 , H1: muD not= 0 
t.test(x,y, alternative="two.sided", paired = TRUE)

# difference between post-training and pre-training scores
d <- y-x
#check for outliers
boxplot(d)
#assess normality assumptions of x and y
qqnorm(d, ylab = "d Sample Quantiles")
shapiro.test(x)