# 8.7
n     <- 25
c     <- 0.08^2
s     <- 0.1
alpha <- 0.05

#• Testovani kritickym oborem
(t0 <- (n-1)*s^2/c)
qchisq(alpha/2, n-1)
qchisq(1-alpha/2, n-1)

# Testovani intervalem spolehlivosti
(dh <- (n-1)*s^2/qchisq(1-alpha/2, n-1))
(hh <- (n-1)*s^2/qchisq(alpha/2, n-1))

# Testovani p-hodnotou
p1 <- pchisq(t0, n-1)
p2 <- 1-pchisq(t0, n-1)
2*min(p1, p2)

# 8.9
X <- c(1.8, 1.0, 2.2, 0.9, 1.5, 1.6) # leva pneumatika
Y <- c(1.5, 1.1, 2.0, 1.1, 1.4, 1.4) # prava pneumatika
Z <- X-Y                             # rozdily

# Test normality
shapiro.test(Z)

#------------------
m <- mean(Z)
s <- sd(Z)
n <- length(Z)
c <- 0

# Testovani kritickym oborem
(t0 <- (m-c)/(s/sqrt(n)))
qt(alpha/2, n-1)
#-qt(1-alpha/2, n-1)
qt(1-alpha/2, n-1)

# IS dopocitat doma

# Tetsovani p-hodnotou
p1 <- pt(t0, n-1)
p2 <- 1-pt(t0, n-1)
2*min(p1, p2)

# 9.2
X <- c(62, 54, 55, 60, 53, 58) # prirustky prasatek krmenych dietou c.1
Y <- c(52, 56, 49, 50, 51)      # prirustky prasatek krmenych dietou c.1

# Testy normality
shapiro.test(X) 
shapiro.test(Y)

s1 <- sd(X)
s2 <- sd(Y)
n1 <- length(X)
n2 <- length(Y)
alpha <- 0.05

# Testovani kritickym oborem
(t0 <- s1^2/s2^2)
qf(1-alpha/2, n1-1, n2-1)
qf(alpha/2, n1-1, n2-1)

# Tetsovani pomoci IS
(dh <- (s1^2/s2^2)/qf(1-alpha/2, n1-1,n2-1))
(hh <- (s1^2/s2^2)/qf(alpha/2, n1-1, n2-1))

# Testovani p-hodnotou
p1 <- pf(t0, n1-1, n2-1)
p2 <- 1-pf(t0, n1-1, n2-1)
2*min(p1,p2)