#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
#
# Computations used for the problems in this section of the text.
#
#-----

# Ex 7.33
#
DF = read.csv( "../../Data/CH07/ex7-33.txt", header=TRUE, quote="'" )
boxplot( DF$polymerization )
qqnorm( DF$polymerization )
qqline( DF$polymerization )
grid()

# Construct the requested confidence interval:
#
n = length( DF$polymerization )
xbar = mean( DF$polymerization )
s = sd( DF$polymerization )
t_crit = qt( 1 - 0.05/2, n-1 )
xbar + ( s / sqrt(n) ) * t_crit * c(-1,+1)


# Ex 7.34
#
n = 14
xbar = 8.48
s = 0.79
t_crit = qt( 1 - 0.05, n-1 )
xbar - ( s / sqrt(n) ) * t_crit

s_prediction = s * sqrt( 1 + 1 / n )
xbar - s_prediction * t_crit


# Ex 7.35
#
n = 15
xbar = 25.0
s = 3.5
t_crit = qt( 1 - 0.05/2, n-1 )
xbar + ( s / sqrt(n) ) * t_crit * c(-1,+1) # CI

s_prediction = s * sqrt( 1 + 1/n )
xbar + s_prediction * t_crit * c(-1,+1) # PI


# Ex 7.36
#
n = 26
xbar = 370.69
s = 24.36
t_crit = qt( 1 - 0.05, n-1 )
xbar + ( s / sqrt(n) ) * t_crit # upper CI limit

s_prediction = s * sqrt( 1 + 1/n )
xbar + s_prediction * t_crit # upper PI limit

s_prediction_x_new = s * sqrt( 1/2 + 1/n )
t_crit = qt( 1 - 0.05/2, n-1 )
xbar + s_prediction_x_new * t_crit * c(-1,+1) # two-sided PI


# Ex 7.37
#
DF = read.csv( "../../Data/CH07/ex7-37.txt", header=TRUE, quote="'" )
qqnorm( DF$cadence )
qqline( DF$cadence )

n = 20
xbar = 0.9255
s = 0.0809
t_crit = qt( 1 - 0.05/2, n-1 )
xbar + ( s / sqrt(n) ) * t_crit * c(-1,+1)

s_prediction = s * sqrt( 1 + 1/n )
xbar + s_prediction * t_crit * c(-1,+1)

install.packages( c("tolerance"), dependencies=TRUE )   
library(tolerance)
normtol.int( DF$cadence, alpha=0.05, P=0.99 )


# Ex 7.38
#
n = 25
xbar = 0.0635
s = 0.0065
t_crit = qt( 1 - 0.05/2, n-1 )

s_prediction = s * sqrt( 1 + 1/n )
xbar + s_prediction * t_crit * c(-1,+1) # two-sided PI

s_tolerance = 2.972
xbar + s_tolerance * s * c(-1,+1)


# Ex 7.39
#
DF = read.csv( "../../Data/CH01/ex01-72.txt", header=TRUE, quote="'" )
Healthy = DF[ DF$Health_status == "Healthy", ]

qqnorm(Healthy$volume)
qqline(Healthy$volume)

normtol.int( Healthy$volume, alpha=0.05, P=0.95, side=2 )

V = Healthy$volume
n = length(V)
xbar = mean(V)
s = sd(V)
t_crit = qt( 1 - 0.05/2, n-1 )

s_prediction = s * sqrt( 1 + 1/n )
xbar + s_prediction * t_crit * c(-1,+1) # two-sided PI


# Ex 7.40
#
DF = read.csv( "../../Data/CH01/ex01-13.txt", header=TRUE, quote="'" )

qqnorm(DF$strength)
qqline(DF$strength)

S = DF$strength
n = length(S)
xbar = mean(S)
s = sd(S)
t_crit = qt( 1 - 0.05, n-1 ) # we want a single lower bound 

xbar - s * sqrt( 1 + 1/n ) * t_crit # lower PI end point