### 1. zadatak


?prop.test()


prop.test(224, n = 300, p = 0.7,
          alternative = "greater", correct = F)





install.packages("pwr")
library(pwr)


?pwr.p.test()


pwr.p.test(h = ES.h(p1 = 0.75, p2 = 0.7),
           n = 300, alternative = "greater")

# u helpu pise da je h = effect size
# to je velicina koja na neki nacin mjeri
# koliko je stvarna vrijednost proporcije
# "udaljena" od onoga sto smo testirali

# ES.h ( p1, p2)
# pri cemu je p1 stvarno
# a p2 je ono sto smo testirali





### 2. zadatak

prop.test(10, n = 200, p = 0.09, 
          alternative = "less", correct = F)


pwr.p.test(h = ES.h(p1 = 0.07, p2 = 0.09), 
           n = 200, alternative = "less")






### 6. zadatak


bolivija <- c(5.62, 5.33, 4.75, 5.96, 4.99, 5.72)
nb <- length(bolivija)
hrv <- c(4.34, 5.21, 5.12, 4.88)
nh <- length(hrv)

(b <- mean(bolivija))
(h <- mean(hrv))
(sb <- sd(bolivija))
(sh <- sd(hrv))
(st_dev <- sqrt((5*sb^2+3*sh^2)/(nb + nh -2)))
(t <- 1/(sqrt(1/nb + 1/nh)) * (b-h) / st_dev)

qt(0.1, df = nb + nh - 2)
qt(0.9, df = nb + nh - 2)

t.test(bolivija, hrv, var.equal = TRUE, 
       conf.level = 0.9, alternative = "greater")

t.test(bolivija, hrv, var.equal = FALSE, 
       conf.level = 0.9, alternative = "greater")
# verzija za test ako nemamo informaciju 
# o jednakosti varijanci -> Welch t-test



### 7. zadatak

mladji <- c(10, 10, 11, 15, 7, 11, 10, 9)
stariji <- c(4, 8, 7, 7, 4, 5, 1, 7, 4, 10, 5)

mean(mladji)
mean(stariji)
sd(mladji)
sd(stariji)
st_dev <- sqrt((7 * var(mladji) + 10 * var(stariji)) / (17))

1/sqrt(1/8 + 1/10) * (mean(mladji) - mean(stariji)) / st_dev
qt(0.05, df = 17)


t.test(mladji, stariji, var.equal = TRUE, 
       conf.level = 0.9, alternative = "two.sided")



### 8. zadatak



tlak1 <- c(138, 145, 130, 150, 144, 128, 133, 149)
tlak2 <- c(135, 140, 132, 146, 144, 130, 131, 142)
d <- tlak1 - tlak2
mean(d)
sd(d)

mean(d) * sqrt(8) / sd(d)
qt(0.99, df = 7)


t.test(tlak1, tlak2, paired = TRUE, var.equal = TRUE, 
       conf.level = 0.99, alternative = "greater")



### 9. zadatak

metoda1 <- c(1.186, 1.153, 1.332, 1.339, 1.2, 1.402, 1.365, 1.537, 1.559)
metoda2 <- c(1.061, 0.992, 1.063, 1.062, 1.065, 1.178, 1.037, 1.086, 1.052)
mean(metoda1-metoda2)/sd(metoda1-metoda2) * sqrt(length(metoda1))
qt(0.025, df = length(metoda1)-1)

t.test(metoda1, metoda2, paired = TRUE, var.equal = TRUE, 
       conf.level = 0.95, alternative = "two.sided")