#################
### SEDMI CAS ###
#################

#1.
19*21.12/c(qchisq(p = 1-0.01/2, df = 19), qchisq(p = 0.01/2, df = 19)) #dvostrani
c(19*21.12/qchisq(0.99, df = 19),Inf) #jednostrani gornji
c(0,19*21.12/qchisq(0.01, df = 19)) # jednostrani donji

#2.
cene <- c(1.22, 1.37, 1.27, 1.20, 1.42, 1.41, 1.22, 1.24,
          1.28, 1.42, 1.48, 1.32, 1.40, 1.26, 1.39, 1.45,
          1.44, 1.49, 1.47, 1.47, 1.24, 1.34, 1.27, 1.35,
          1.34, 1.45, 1.49, 1.45, 1.23, 1.20, 1.42, 1.34,
          1.43, 1.21, 1.49, 1.36, 1.24, 1.20, 1.45,
          1.23, 1.25, 1.24, 1.35, 1.23, 1.39, 1.38,
          1.46, 1.48, 1.26, 1.36, 1.22, 1.46, 1.39,
          1.22, 1.29, 1.47, 1.24, 1.35, 1.21, 1.21)
cene
xn <- mean(cene)
sn2 <- var(cene)
n <- length(cene)
beta1 <- 0.95
beta2 <- 0.97
c1 <- qt(beta1+(1-beta1)/2, df=n-1) 
int.pov.m <- c(xn-c1*sqrt(sn2)/sqrt(n), xn+ c1*sqrt(sn2)/sqrt(n) )
int.pov.m
c2 <- qchisq(beta2, df=n-1)
int.pov.sigma2 <- c((n-1)*sn2/c2, Inf)
int.pov.sigma2
int.pov.sigma <- c(sqrt((n-1)*sn2/c2), Inf)
int.pov.sigma

#3.
library(EnvStats)
varTest(cene, sigma.squared = 0.02, alternative = "less")
# ZAKLJUCAK???

#5.
285/500+c(qnorm(0.05),qnorm(0.95))*sqrt(285/500*215/500/500)

#8.
prop.test(x = 30, n = 72, p = 0.5, alternative = "two.sided", conf.level = 0.95)

#10.

uzorak <- PopisStanovnistva[sample(1:400,20),] #uzorak 
uzorak$sport