varS <- function(x,nj, myMean) {
  for(i in 1:length(x)) {
    x[i] <- ((x[i] - myMean)^2)*nj[i]
  }
  s <- sum(x)/(sum(nj)-1)
}
true_value_sig <- function(n, alpha=0.05, s) {
  a <- (n-1)*s^2/ qchisq(1-alpha/2, n-1)
  b <- (n-1)*s^2/ qchisq(alpha/2, n-1)
  c(a,b)
}

srednia<- 1/180*(0.2*25+ 0.6*50+1*40 + 1.4*35+ 1.8*30)
x <- c(0.2, 0.6, 1, 1.4, 1.8)
nj <- c(25,50,40,35,30)
myS <- sqrt(varS(x,nj, srednia))
(true_value_m(180,alpha=0.1,srednia,s=myS))
# Ans.: 0.9245566 1.0532212
(sqrt(true_value_sig(180, alpha=0.1, s=myS)))
# Ans.: (0.4805589, 0.5720536)