#Pr.c.1 - Alternativni rozdeleni
n     <- 150
alpha <- 0.05
c     <- 0.3
M     <- 38/n
#H0: theta = 0.3
#H1: theta < 0.3


#Testovani kritickym oborem
(t0   <- (M-c)/sqrt(c*(1-c)/n)) #testovaci statistika
-qnorm(1-alpha)                 #horni hranice kritickeho oboru
#W = ( -infty ; -1.645)
#t0 = -1.247 nenalezi do kritickeho oboru W => H0 nezamitame na asymptoticke hladine vyznamnosti alpha=0.05.

#Testovani pomoci IS
(hh   <- M-sqrt(M*(1-M)/n)*qnorm(alpha)) #horni hranice IS
#95% IS pro parametr theta je (-infty , 0.3117)
#0.3 nalezi do IS => H0 nezamitame na asymptoticke hladine vyznamnosti alpha=0.05.


#Pr.c.2 - podil dvou rozptylu:
X1 <- c(62,54,55,60,53,58)
X2 <- c(52,56,49,50,51)
s1 <- sd(X1)
s2 <- sd(X2)
#H0: s1^2/s2^2=1
#H1: s1^2/s2^2 se nerovna 1

#Testovani kritickym oborem
(t0 <- s1^2/s2^2) #testovaci statistika
alpha <- 0.05
n1    <- length(X1)
n2    <- length(X2)
qf(alpha/2,n1-1,n2-1)    
qf(1-alpha/2,n1-1,n2-1)
#Kriticky obor ma tvar: W=(-infty ; 0.1354> U <9.3645 ; infty)
#t0 = 1.7534 nenalezi do IS => H0 nezamitame na hladine vyznamnosti alpha=0.05.

#Testovani pomoci IS
(dh <- (s1^2/s2^2)/qf(1-alpha/2,n1-1,n2-1)) #dolni hranice IS
(hh <- (s1^2/s2^2)/qf(alpha/2,n1-1,n2-1))   #horni hranice IS
#IS ma tvar (0.1872 ; 12.9541)
#1 nalezi do IS => H0 nezamitame na hladine vyznamnosti alpha=0.05.