#8.4
1-pnorm(80, 72, sqrt(8.1))

# 7.5
m     <- 139.13
sigma <- sqrt(39.112)
n     <- 15
c     <- 142
alpha <- 0.05

# Kriticky obor
(t0 <- (m-c)/(sigma/sqrt(n)))
(w1 <- -qnorm(1-alpha))

# IS
(hh <- m-sigma/sqrt(n)*qnorm(alpha))

# p-hodnoty
pnorm(t0)

# 8.1
data <- read.delim('vrstva_stribra.txt')
head(data)
stribro <- data$tloustka_vrstvy
shapiro.test(stribro)           # vystupem bude defaultni vystup

ls(shapiro.test(stribro))
shapiro.test(stribro)$p.value   # vystupem bude pouze p-hodnota


library(nortest)
lillie.test(stribro)            # Lillie-Forsuv test
lillie.test(stribro)$p.value

ad.test(stribro)                # Anderson-Darlinguv test
ad.test(stribro)$p.value

# Q-Q plot
qqnorm(stribro, main='Q-Q graf', 
       xlab='teoreticke kvantily', ylab='pozorovne kvantily', 
       col='darkblue', pch=15)
qqline(stribro, col='red', lwd=2)