#
# 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.
# 
#-----

# Problem 2:
# 
pc = c( 0.80, 0.92, 0.98 ) # the probability coverages 
alpha = 1 - pc

c = qnorm( 1 - alpha/2 )


# Problem 3:
#
alpha = 0.05
c = qnorm( 1 - 0.5*alpha )

xbar = 45
n = 25
sigma = 5 
xbar - c * sigma/ sqrt(n)
xbar + c * sigma/ sqrt(n)


# Problem 5:
#
alpha = 0.05
c = qnorm( 1 - 0.5*alpha )

xbar = 1150
n = 36
sigma = 25
xbar - c * sigma/ sqrt(n)
xbar + c * sigma/ sqrt(n)


# Problem 8:
#
s = c(20.01,19.88,20.00,19.99)
pc = 0.95
alpha = 1 - pc
sigma = 0.01
n = length(s)

xbar = mean(s)
xbar - ( sigma / sqrt(n) ) * qnorm( 1 - 0.5 * alpha )
xbar + ( sigma / sqrt(n) ) * qnorm( 1 - 0.5 * alpha )


# Problem 12:
#
# Part (a):
# 
n = 10
xbar = 26
s = 9
alpha = 0.05

xbar - qt( 1 - 0.5*alpha, n-1 ) * ( s / sqrt(n) )
xbar + qt( 1 - 0.5*alpha, n-1 ) * ( s / sqrt(n) )

# Problem 15:
#
s = c( 5,12,23,24,18,9,18,11,36,15 )

xbar = mean(s)
sbar = sqrt(var(s))
n = length(s) 
alpha = 0.05

xbar - qt( 1 - 0.5*alpha, n-1 ) * ( sbar / sqrt(n) )
xbar + qt( 1 - 0.5*alpha, n-1 ) * ( sbar / sqrt(n) )

# Problem 16:
#
M = 34
S_M = 3
alpha = 0.05
c = qnorm( 1 - 0.5 * alpha )
M - c * S_M
M + c * S_M


# Problem 18:
#
pbinom(8,10,0.5) - pbinom(1,10,0.5) 


# Problem 19:
#
pbinom(11,15,0.5) - pbinom(3,15,0.5) 


# Problem 20:
#
dt = c( 77, 87, 88, 114, 151, 210, 219, 246, 253, 262, 296, 299, 306, 376, 428, 515, 666, 1310, 2611)
sdt = sort(dt)
k = which(sdt==88)
n = length(sdt)
pbinom(16,n,0.5) - pbinom(2,n,0.5) 


# Problem 34:
#
data = c( 545, 555, 558, 572, 575, 576, 578, 580, 594, 605, 635, 651, 653, 661, 666 )

postscript("../../WriteUp/Graphics/Chapter6/prob_34_boxplot.eps", onefile=FALSE, horizontal=FALSE)
boxplot( data )
dev.off()

# Problem 35:
#
alpha = 0.05
c = qnorm( 1 - 0.5 * alpha )
n = 24
xt = 52
sw2 = 12

print( sprintf( "%10.6f", xt - c * sqrt(sw2)/(0.6*sqrt(n)) ) ) 
print( sprintf( "%10.6f", xt + c * sqrt(sw2)/(0.6*sqrt(n)) ) )


# Problem 37:
#
source('../Chapter2/winsorize.R')
source('../Chapter2/tmean.R')
data   = c( 59,106,174,207,219,237,313,365,458,497,515,529,557,615,625,645,973,1065,3215 )

n = length(data)

# 95% CI for the the population mean:
alpha = 0.05
xbar  = mean( data )
sbar  = sqrt(var(data))

print( sprintf( "%10.6f", xbar - qt( 1 - 0.5*alpha, n-1 ) * ( sbar / sqrt(n) ) ) ) 
print( sprintf( "%10.6f", xbar + qt( 1 - 0.5*alpha, n-1 ) * ( sbar / sqrt(n) ) ) ) 

# 95% CI for the 20% trimmed mean: 
xbart  = tmean( data, p=0.2 )
data_w = winsorize( data, p=0.2 ) 
sw2    = var( data_w ) 

c = qnorm( 1 - 0.5 * alpha )

print( sprintf( "%10.6f", xbart - c * sqrt(sw2)/(0.6*sqrt(n)) ) ) 
print( sprintf( "%10.6f", xbart + c * sqrt(sw2)/(0.6*sqrt(n)) ) )


# Problem 39:
#
source('../Chapter2/winsorize.R')
source('../Chapter2/tmean.R')
data = c( 5,60,43,56,32,43,47,79,39,41 )

n = length(data)

# 95% CI for the the population mean:
alpha = 0.05
xbar  = mean( data )
sbar  = sqrt(var(data))

print( sprintf( "%10.6f", xbar - qt( 1 - 0.5*alpha, n-1 ) * ( sbar / sqrt(n) ) ) ) 
print( sprintf( "%10.6f", xbar + qt( 1 - 0.5*alpha, n-1 ) * ( sbar / sqrt(n) ) ) ) 

# 95% CI for the 20% trimmed mean: 
xbart  = tmean( data, p=0.2 )
data_w = winsorize( data, p=0.2 ) 
sw2    = var( data_w ) 

c = qnorm( 1 - 0.5 * alpha )

print( sprintf( "%10.6f", xbart - c * sqrt(sw2)/(0.6*sqrt(n)) ) ) 
print( sprintf( "%10.6f", xbart + c * sqrt(sw2)/(0.6*sqrt(n)) ) )