# Problems on EPage 474
#

# Section 3; Question 1:
#
large_sales = c( 21, 23, 13, 22, 7, 17, 19, 11, 2, 30, 15, 43 ) #=X
small_sales = c( 21, 21, 14, 31, 19, 19, 11, 29, 20, 27, 27, 24 ) #=Y

n = length( large_sales )
m = length( small_sales )
sx2 = var( large_sales )
sy2 = var( small_sales )
f = sy2/sx2

alpha = 0.05
f_crit_L = qf( alpha/2, m-1, n-1 )
f_crit_R = qf( 1-alpha/2, m-1, n-1 )
print(sprintf('alpha= %.2f; f_crit_L=%.6f; f_crit_R= %.6f; f= %.6f', alpha, f_crit_L, f_crit_R, f))


# Section 3; Question 2:
#
fixed = c( 5.5, 5.5, 5.25, 5.125, 5.875, 5.625, 5.25, 4.875 ) #=X
arm = c( 3.875, 5.125, 5.0, 4.75, 4.375 ) #=Y

n = length( fixed )
m = length( arm )
sx2 = var( fixed )
sy2 = var( arm )
f = sy2/sx2

alpha = 0.1
f_crit_L = qf( alpha/2, m-1, n-1 )
f_crit_R = qf( 1-alpha/2, m-1, n-1 )

print(sprintf('alpha= %.2f; f_crit_L= %.6f; f_crit_R= %.6f; f=%.6f', alpha, f_crit_L, f_crit_R, f))


# Section 3; Question 3:
#
normal = c( 8, 4, 6, 3, 1, 4, 4, 6, 4, 2, 2, 1, 1, 4, 3, 3, 2, 6, 3, 4 )
schizophrenic = c( 2, 1, 1, 3, 2, 7, 2, 1, 3, 1, 0, 2, 4, 2, 3, 3, 0, 1, 2, 2 )

n = length( normal )
m = length( schizophrenic )
sx2 = var( normal )
sy2 = var( schizophrenic )
f = sy2/sx2

alpha = 0.05
f_crit_L = qf( alpha/2, m-1, n-1 )
f_crit_R = qf( 1-alpha/2, m-1, n-1 )
print(sprintf('alpha= %.2f; f_crit_L= %.6f; f_crit_R= %.6f; f=%.6f', alpha, f_crit_L, f_crit_R, f))

# Now test if mu_X = mu_Y:
#
xbar = mean( normal )
ybar = mean( schizophrenic )
sp2 = ( (n-1)*sx2 + (m-1)*sy2 ) / ( n+m-2 )
t = ( xbar - ybar )/sqrt( sp2*(1/n + 1/m) )

p_value = 2*(1-pt(abs(t), n+m-2)) # two-sided test

alpha = 0.05
t_crit = qt( 1-alpha/2, n+m-2 )
print(sprintf('t= %.6f; p_value= %.6f; t_crit= %.6f', t, p_value, t_crit))


# Section 3; Question 4:
#
source('chap_9_sect_3_question_4_data.R')

n = length( control )
m = length( test )
sx2 = var( control )
sy2 = var( test )

f = sy2/sx2

alpha = 0.05
f_crit_L = qf( alpha/2, m-1, n-1 )
f_crit_R = qf( 1-alpha/2, m-1, n-1 )
print(sprintf('alpha= %.2f; f_crit_L= %.6f; f_crit_R= %.6f; f=%.6f', alpha, f_crit_L, f_crit_R, f))


# Section 3; Question 5:
#
source('chap_9_sect_3_question_5_data.R')

n = length( normal )
m = length( raynauds )
sx2 = var( normal )
sy2 = var( raynauds )

f = sy2/sx2

alpha = 0.05
f_crit_L = qf( alpha/2, m-1, n-1 )
f_crit_R = qf( 1-alpha/2, m-1, n-1 )
print(sprintf('alpha= %.2f; f_crit_L= %.6f; f_crit_R= %.6f; f= %.6f', alpha, f_crit_L, f_crit_R, f))


# Section 3; Question 6:
#
source('chap_9_sect_3_question_6_data.R')

n = length( american )
m = length( national )
sx2 = var( american )
sy2 = var( national )
f = sy2/sx2

alpha = 0.05
f_crit_L = qf( alpha/2, m-1, n-1 )
f_crit_R = qf( 1-alpha/2, m-1, n-1 )
print(sprintf('alpha= %.2f; f_crit_L= %.6f; f_crit_R= %.6f; f= %.6f', alpha, f_crit_L, f_crit_R, f))


# Section 3; Question 7:
#
source('chap_9_sect_2_question_8_data.R')

X = DF[ DF$Sex=='F', ]
n = dim(X)[1]
sx2 = var(X$Halflife)

Y = DF[ DF$Sex=='M', ]
m = dim(Y)[1]
sy2 = var(Y$Halflife)

f = sy2/sx2

alpha = 0.05
f_crit_L = qf( alpha/2, m-1, n-1 )
f_crit_R = qf( 1-alpha/2, m-1, n-1 )
print(sprintf('alpha= %.2f; f_crit_L= %.6f; f_crit_R= %.6f; f=%.6f', alpha, f_crit_L, f_crit_R, f))


# Section 3; Question 8:
#
source('chap_9_sect_3_question_8_data.R')

n = length( african_american )
m = length( white )
sx2 = var( african_american )
sy2 = var( white )
f = sy2/sx2

alpha = 0.05
f_crit_L = qf( alpha/2, m-1, n-1 )
f_crit_R = qf( 1-alpha/2, m-1, n-1 )
print(sprintf('alpha= %.2f; f_crit_L= %.6f; f_crit_R= %.6f; f= %.6f', alpha, f_crit_L, f_crit_R, f))