## Solutions to exercises

### PART 1 ###

# Loading data
days = scan("pr0220.txt")
# (a), (b), (c)
# One sided hypothesis - we can assume the average is smaller than 120
# and try to reject this
# H0: mu <= 120
# H1: mu > 120
t.test(days,mu=120,conf.level=0.99,alternative="greater")
# ignore the confidence interval here, it is not the one we are looking for
# (d)
t.test(days,mu=120,conf.level=0.99)
# here we have the right confidence interval
# We clean up
rm(list=ls())

### PART 2 ###

# Data
values = scan("pr0225.txt")
# The order of data is with alternating treatments
# Here is a way to extract the two treatments:
x = values[c(1, 3, 5, 7, 9, 11, 13, 15, 17, 19)]
y = values[seq(2, 20, 2)]  # A bit more sophisticated!
# We do the tests
var.test(x, y)                # p=0.97, accept (suspiciously high!)
t.test(x, y, var.equal=TRUE)  # p=0.96, accept (the same!)
# These high p-values are "too good to be true".  I think that this
# experiment has never really been made, only in Montgomery's mind!
# Now solution to Question (c):
# Normality assumed, but not critical for t-tests. Due to the central
# limit theorem, means of ten closer to normality than individual data
# Anyhow, let's do the normality check:
qqnorm(x); qqline(x, col="green")  # Looks tolerable
qqnorm(y); qqline(y, col="green")  # Looks nice
# Cleaning
rm(list=ls())