# Questions on EPage 399
#

# Section 4; Question 1:
#
ans = c( 1 - pt(1.134, 6), pt(0.866, 15), 1-pt(-1.25, 3), pt(2.462, 29) - pt(-1.055, 29) )
print(ans)


# Section 4; Question 2:
#
ans = c( qt( (1+0.98)/2, 22 ), qt( 0.15, 13 ), qt( 0.95, 26 ), qt( 1-0.025, 2) )
print(ans)


# Question 3:
#
n = 10
pt_1 = qt( 1-0.05, n )-qt( 1-0.1, n )
pt_2 = qt( 1-0.1, n )-qt( 1-0.15, n )
print( c( pt_1, pt_2 ) )


# Question 4:
#
n = 9
print( c( qt( 1-0.1, n-1 ), qt( 1-0.05, n-1 ) ) )


# Question 5:
#
n = 11
print( qt( 1-0.05/2, n-1 ) )


# Question 6:
#
n = 20
t_crit = qt( 1-0.01/2, n-1 )
print( t_crit / sqrt(n) )


# Question 7:
#
source('chap_7_sect_4_question_7_data.R')
n = length(data)
xbar = mean(data)
s = sd(data)
t_crit = qt( 1-0.1/2, n-1 )
ci = xbar + t_crit * ( s / sqrt(n) ) * c( -1, +1 )
print( ci )



# Question 8:
#
source('chap_7_sect_4_question_8_data.R')
print( t.test( DF$Repair_Cost, conf.level=0.95 ) )


# Question 9:
#
source('chap_7_sect_4_question_9_data.R')
print( t.test( DF$age, conf.level=0.95 ) )
plot( DF$year, DF$age, type='p', pch=19, cex=1.5, xlab='year', ylab='age' )
abline(h=mean(DF$age), col='blue')
grid()


# Question 10:
#
n = 61
sum_y = 6450
sum_y2 = 684900
ybar = sum_y / n
var_y = sum_y2 / n - ybar^2
s = sqrt(var_y)
t_crit = qt( 1-0.01/2, n-1 )
ci = ybar + t_crit * ( s / sqrt(n) ) * c(-1, +1)
print( ci )


# Question 11:
#
n = 24
sum_y = 4645
sum_y2 = 959265
ybar = sum_y / n
ci = ybar + t_crit * ( s / sqrt(n) )
var_y = sum_y2 / n - ybar^2
s = sqrt(var_y)
t_crit = qt( 1-0.1/2, n-1 )
ci = ybar + t_crit * ( s / sqrt(n) ) * c(-1, +1) 
print( ci )


# Question 12:
#
n = 16
ci = c( 44.7, 49.9 )
ybar = mean(ci)
t_crit = qt( 1-0.05/2, n-1 )
s = diff( ci ) / ( 2 * t_crit / sqrt(n) )
print( c( ybar, s ) )


# Question 14:
#
n = 9
xbar = 59540
s = 6860
t_crit = qt( 1-0.05/2, n-1 ) 
ci = xbar + t_crit * ( s / sqrt(n) ) * c(-1, +1) 
print( ci )


# Question 15:
#
n = 20
pt_a = pt( 2.0930, n-1 ) - pt( -2.0930, n-1 ) 

n = 15
pt_b = pt( 1.345, n-1 ) - pt( -1.345, n-1 )

n = 27
pt_c = pt( 2.7787, n-1 ) - pt( -1.7056, n-1 )

n = 21
pt_d = pt( 1.7247, n-1 )

print( c( pt_a, pt_b, pt_c, pt_d ) )


# Question 16:
#
n = 336
sum_y = 1392.6
sum_y2 = 10518.84
ybar = sum_y / n
var_y = sum_y2 / n - ybar^2
s = sqrt(var_y)
t_crit = qt( 1-0.05/2, n-1 )
ci = ybar + t_crit * ( s / sqrt(n) ) * c( -1, +1 )
print( ci )


# Question 17:
#
source('../Chapter5/chap_5_sect_3_question_2_data.R')
n = length(DF$Ratio)
m = mean(DF$Ratio)
s = sd(DF$Ratio)
t = (m-0.8) / (s/sqrt(n))
p_value = 2*(1-pt(abs(t), n-1)) # two-sided test
print( sprintf('t= %f; p_value= %f', t, p_value) )


# Question 18:
#
n = 84
ybar = 143.8
mu_0 = 132.4
s = 6.0
t = (ybar-mu_0)/(s/sqrt(n))
p_value = 2*(1-pt(abs(t), n-1)) # two-sided test
print( sprintf('t= %f; p_value= %f', t, p_value) )


# Question 19:
#
source('chap_7_sect_4_question_19_data.R')
print( t.test( DF$y, mu=40 ) )


# Question 20:
#
source('chap_7_sect_4_question_20_data.R')
print( t.test( DF$Ratio_Width_to_Height, mu=0.618 ) )


# Question 21:
#
data = c( 0.0039, 0.0041, 0.0038, 0.0044, 0.0040, 0.0036, 0.0034, 0.0036, 0.0046, 0.0036 )
print( t.test( data, mu=0.0042, alternative='less' ) )