# Confidence interval:
x = c(3062.6, 3062.8, 3062.8, 3063.1, 3063, 3062.7, 3062.7, 3062.5, 3062.9); x
a = 0.05; g = 1-a; a; g;
n = length(x); n
kvt = qt((1+g)/2, n-1); kvt
m = mean(x); m
v = var(x); v
m_D2 = m - kvt*sqrt(v) / sqrt(n); m_D2
m_H2 = m + kvt*sqrt(v) / sqrt(n); m_H2
#  <=>:
tt = t.test(x, conf.level = 0.95, alternative = "two.sided"); tt
tt$conf.int[c(1,2)]

tt[1]
for(i in 1:3) {print(tt[i]);}  # The for loop in R is what we call a foreach loop
# =>
tt[4]

kvc1 =  qchisq((1-g)/2, n-1); kvc1
kvc2 =  qchisq((1+g)/2, n-1); kvc2
d_D2 = v * (n-1) / kvc2; d_D2
d_H2 = v * (n-1) / kvc1; d_H2


?t.test
t.test(x, y = NULL,
       alternative = c("two.sided", "less", "greater"),
       mu = 0, paired = FALSE, var.equal = FALSE,
       conf.level = 0.95, ...)
### vykona aj jedno aj dvojvyberovy t-test

x = c(1.6, 1.88, 2.1, 1.66, 1.93, 1.73, 1.74, 2.07)
# 1) H0: m = 1.75,  alfa = 0.05
t.test(x, y = NULL, alternative = "greater", mu = 1.75)  #, conf.level = 1-0.05)
# 2) H0: m = 1.7,  alfa = 0.05
t.test(x, y = NULL, alternative = "greater", mu = 1.7)   #, conf.level = 1-0.05)
# 3) H0: m = 1.7,  alfa = 0.11
t.test(x, y = NULL, alternative = "greater", mu = 1.75)  #, conf.level = 1-0.11)


?var.test
var.test(x, y, ratio = 1,
         alternative = c("two.sided", "less", "greater"),
         conf.level = 0.95, ...)
### vykona len dvojvyberovy F-test - zial


DomUloha:
==========
V R napiste funkciu na vypocet
- intervalu spolahlivosti m
- intervalu spolahlivosti s^2
- testovanie hypotez o m
	a) pomocou vzorca
	b) pomocou t.test
- testovanie hypotez o s^2