#
# 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.
# 
#-----

print("Problem 14:")
# 
n1 = 15
N1 = 24

n2 = 23
N2 = 42

p1 = n1/N1
p2 = n2/N2

sq_se = p1*(1-p1)/N1 + p2*(1-p2)/N2

Z = (p1 - p2)/sqrt( sq_se )

print( Z )

alpha = 0.05
print( qnorm( 1 - 0.5*alpha ) )


print( "Problem 15:")
# 
n1 = 40
N1 = 98

n2 = 30
N2 = 70

p1 = n1/N1
p2 = n2/N2

sq_se = p1*(1-p1)/N1 + p2*(1-p2)/N2

Z = (p1 - p2)/sqrt( sq_se )  # they do not differ significantly

print( Z )

alpha = 0.05
c = qnorm( 1 - 0.5*alpha ) 
print( c )

ci = c( (p1-p2) - c*sqrt(sq_se), (p1-p2) + c*sqrt(sq_se) )
print( ci )

print( "Problem 16:")
# 
n1 = 20
N1 = 121

n2 = 15
N2 = 80

p1 = n1/N1
p2 = n2/N2

sq_se = p1*(1-p1)/N1 + p2*(1-p2)/N2

Z = (p1 - p2)/sqrt( sq_se )
print( Z )

alpha = 0.05
c = qnorm( 1 - 0.5*alpha ) 
print( c )

ci = c( (p1-p2) - c*sqrt(sq_se), (p1-p2) + c*sqrt(sq_se) )
print( ci )

print( "Problem 18:")
# 
dm = -7.5
ms_se = 3.93
alpha = 0.05
c = qnorm( 1. - 0.5*alpha )
CI = c( dm - c*ms_se, dm + c*ms_se )
print( CI )

print( "Problem 20:")
# 
n1 = 11
N1 = 23

n2 = 10
N2 = 23

p1 = n1/N1
p2 = n2/N2

sq_se = p1*(1-p1)/N1 + p2*(1-p2)/N2

Z = (p1 - p2)/sqrt( sq_se )
print( Z )

alpha = 0.05
c = qnorm( 1 - 0.5*alpha ) 
print( c )

ci = c( (p1-p2) - c*sqrt(sq_se), (p1-p2) + c*sqrt(sq_se) )
print( ci )


print( "Problem 21:")
# 
n = 49
dbar = 3
sd = 4

T_D = dbar/(sd/sqrt(n))
print( T_D )

alpha = 0.05
c = qt( 1 - 0.5*alpha, n-1 ) 
print( c )

ci = c( dbar - c*sd/sqrt(n), dbar + c*sd/sqrt(n) )
print( ci )


print( "Problem 23:")
# 
x = c( 72, 60, 56, 41, 32, 30, 39, 42, 37, 33, 32, 63, 54, 47, 91, 56, 79, 81, 78, 46, 39, 32, 60, 35, 39, 50, 43, 48 )
y = c( 66, 53, 57, 29, 32, 35, 39, 43, 40, 29, 30, 45, 46, 51, 79, 68, 65, 80, 55, 38, 35, 30, 50, 37, 36, 34, 37, 54 )
n = length(x)
print( sprintf("mean(x)= %10.6f; mean(y)= %10.6f",mean(x),mean(y)) )
d = x - y # a vector of differences
dbar = mean(d)
sdsq = var(d)
TD = dbar/( sqrt(sdsq/n) )
print( TD ) 

t = qt( 1 - 0.5*0.05, n-1 )
print(t)

CI = c( dbar - c * sqrt( sdsq/n), dbar + c * sqrt( sdsq/n ) )
print( CI ) 

print( "Problem 24:")
# 
M_D = 5
S_D = 2
c = qnorm( 1 - 0.5*0.05 )
CI = c( M_D - c * S_D, M_D + c * S_D ) 
print( CI )