library(stats)

# Section 3; Question 2:
#
k0 = 35
k1 = 55
k2 = 10
xs = c( k0, k1, k2 )
n = k0 + k1 + k2
prob = dhyper( 0:2, 4, 6, 2 )
expected_frequency = n * prob
t = length( prob )
d = sum( (xs - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.1, t-1 )

p_value = 1 - pchisq( d, t-1 )
print( sprintf('d= %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )


# Section 3; Question 3:
#
prob = dbinom( 0:2, 2, 2/5 )
t = length( prob )
expected_frequency = n * prob
d = sum( (xs - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.1, t-1 )
p_value = 1-pchisq( d, t-1 )

print( sprintf('d= %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )


# Section 3; Question 4:
#
n = 2650

k0 = 494 # midnight - 4AM
k1 = n - k0 # 4AM - midnight
xs = c( k0, k1 )

prob = c( 4/24, 20/24 )

t = length( prob )
expected_frequency = n * prob
d = sum( (xs - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.1, t-1 )
p_value = 1-pchisq( d, t-1 )

print( sprintf('d= %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )


# Section 3; Question 5:
#
p0 = 4/24
z = ( xs[1] - n*p0 )/sqrt( n*p0*(1-p0) )

z_crit = qnorm( 1-0.05 )
p_value = 1-pnorm( z )

print( sprintf('z= %f; z_critical= %f; p_value= %f', z, z_crit, p_value) )




# Section 3; Question 6:
#
n = 5139
k0 = 1383
k1 = n - k0
xs = c( k0, k1 )

prob = c( 1/4, 3/4 )
expected_frequency = n * prob

t = length( prob )
d = sum( (xs - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.05, t-1 )
p_value = 1-pchisq( d, t-1 )

print( sprintf('d= %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )


# Section 3; Question 7:
#
source('chap_10_sect_3_question_7_data.R')
xs = DF$Number
n = sum( xs )

prob = c( 0.3, 0.2, 0.2, 0.1, 0.1, 0.1 )
expected_frequency = n * prob

t = length( prob )
d = sum( (xs - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.05, t-1 )
p_value = 1-pchisq( d, t-1 )

print( sprintf('d= %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )


# Section 3; Question 8:
#
source('chap_10_sect_3_question_8_data.R')
n = sum( DF$Number_of_Years )
k = sum( DF$Number_of_Games )
xs = c( k, n-k )

prob = c( 1/2, 1/2 )
expected_frequency = prob * n

t = length(prob)
d = sum( (xs - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.05, t-1 )
p_value = 1-pchisq( d, t-1 )
print( sprintf('d= %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )


# Section 3; Question 9:
#
source('chap_10_sect_3_question_9_data.R')
n = sum( Number_of_Winners )
n_spots = length( Number_of_Winners )

prob = rep( 1/n_spots, n_spots )
expected_frequency = prob * n

xs = Number_of_Winners
t = length(prob)
d = sum( (xs - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.05, t-1 )
p_value = 1-pchisq( d, t-1 )
print( sprintf('d = %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )


# Section 3; Question 10:
#
source('chap_10_sect_3_question_10_data.R')

breaks = seq( from=220, to=300, by=10 )
h = hist( data, breaks, plot=FALSE )

# Compute the expected frequency counts under this binning:
#
m = 266
s = 16
prob = c()
for( ii in 1:(length(breaks)-1) ){
    p = pnorm( (breaks[ii+1]-m)/s ) - pnorm( (breaks[ii]-m)/s )
    prob = c( prob, p )
}

n = length(data)
expected_frequency = n * prob
print( round( expected_frequency, 3 ) )

t = length(prob)
d = sum( (h$counts - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.10, t-1 )
p_value = 1-pchisq( d, t-1 )

print( sprintf('d= %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )


# Section 3; Question 11:
#
prob = c( 1/27, 7/27, 19/27 )

xs = c( 8, 16, 26 )
n = sum( xs ) 

expected_frequency = n * prob
print( round( expected_frequency, 3 ) )

t = length(prob)
d = sum( (xs - expected_frequency)^2 / expected_frequency )
d_crit = qchisq( 1-0.05, t-1 )
p_value = 1-pchisq( d, t-1 )

print( sprintf('d= %f; d_critical= %f; p_value= %f', d, d_crit, p_value) )