#1
t_conf_interval <- function(n, sample_mean, afla, s2 ){
  #se=s/sqrt(n)
  sigma=sqrt(s2)
  critical_t=qt(1-afla/2,n-1)
  a=sample_mean - critical_t*sigma/sqrt(n)
  b=sample_mean + critical_t*sigma/sqrt(n)
  interval=c(a,b)
  print(interval)
}

#2
t_conf_interval(196, 44.65, 0.01, 2.25)

#3
t_conf_interval(49, 12, 0.01, 1.75^2)
t_conf_interval(49, 12, 0.05, 1.75^2)

t_conf_interval(49, 13.5, 0.05, 1.25^2)


#4
t_conf_interval_fisier <- function(afla,filename ){
  x=scan(filename)
  sample_mean=mean(x)
  s=sd(x)
  n=length(x)
  se=s/sqrt(n)
  critical_t=qt(1-afla/2,n-1)
  a=sample_mean - critical_t*s/sqrt(n)
  b=sample_mean + critical_t*s/sqrt(n)
  interval=c(a,b)
  print(interval)
}


#5
t_conf_interval_fisier(0.1, "lab4_sample.txt")
t_conf_interval_fisier(0.05, "lab4_sample.txt")
t_conf_interval_fisier(0.01, "lab4_sample.txt")

#1
test_proportion_sim <- function (alfa, n, succese, p0 ){
  p_prim=succese/n
  z_score=(p_prim-p0)/sqrt(p0*(1-p0)/n)
  critical_z=qnorm(1-alfa/2, 0,1)
  x=c(z_score,critical_z)
  if((abs(z_score)<abs(critical_z))
  {
    print("se accepta ipoteza nula")
  }
  else
  {
    print("se respinge ipoteza nula")
  }
  print(x)
}
#1
test_proportion_stg <- function (alfa, n, succese, p0 ){
  p_prim=succese/n
  z_score=(p_prim-p0)/sqrt(p0*(1-p0)/n)
  critical_z=qnorm(alfa, 0,1)
  x=c(z_score,critical_z)
  if((z_score>critical_z))
  {
    print("se accepta ipoteza nula")
  }
  else
  {
    print("se respinge ipoteza nula")
  }
  print(x)
}
#1
test_proportion_dr <- function (alfa, n, succese, p0 ){
  p_prim=succese/n
  z_score=(p_prim-p0)/sqrt(p0*(1-p0)/n)
  critical_z=qnorm(1-alfa, 0,1)
  x=c(z_score,critical_z)
  if((z_score<critical_z))
  {
    print("se accepta ipoteza nula")
  }
  else
  {
    print("se respinge ipoteza nula")
  }
  print(x)
}

#2
test_proportion_dr(0.05, 150, 20, 0.1)

#3
test_proportion_stg(0.05, 110, 15, 0.1)

#4
test_proportion_dr(0.05, 128, 10, 0.025)

#5
test_proportion_stg(0.01, 42, 17, 0.25)