r l5

#OANA DANIEL

I.1
z_test=function(alfa,p_mean,s_mean,n,sigma)
{
  if(p_mean>s_mean)
  {
    critical_z = qnorm(alfa)
    z_score = (s_mean - p_mean)/(sigma/sqrt(n))
  }
  else
  {
    critical_z = qnorm(1- alfa)
    z_score = (s_mean - p_mean)/(sigma/sqrt(n))
    }

    if(z_score>critical_z)
    {
        cat("H0 respinsa")
    }
    else
    {
        cat("H0 acceptata")
    }
  cat("\n")
  print(z_score)
  print(critical_z)
}

I.2
z_test(0.01,90,90,49,sqrt(144))

I.3
z_test(0.01,75,85,36,sqrt(17))

I.4
z_test(0.01,21,20.5,100,2.5)

I.5
z_test(0.05,1000,970,100,85)
z_test(0.01,1000,970,100,85)

I.6
z_test(0.01,22,20,16,3)


II.1
t_test=function(filename,alfa,p_mean)
{
  a=citire(filename)
  b=calcul(a);n=b[1]
  s_mean=b[2]
  sigma=b[3]
  if(p_mean>s_mean)
  {
    critical_t = qt(alfa,n-1)
    t_score = (s_mean - p_mean)/(sigma/sqrt(n))
    }
  else
  {
    critical_t = qt(1- alfa,n-1)
    t_score = (s_mean - p_mean)/(sigma/sqrt(n))
    }
  if(t_score>critical_t)
  {
    cat("H0 respinsa")
  }
  else
  {
    cat("H0 acceptata")
  }
  cat("\n")
  print(t_score)
  print(critical_t)
}

calcul=function(a)
{
  n=length(a)
  media=mean(a)
  s=sd(a)
  b<-c(n,media,s)
}

citire=function(fisier)
{
  a<-scan(fisier)
}

II.2
t_test("vector.txt",0.01,34)

II.3
z_test(0.01,11.4,11.9,100,0.25)
z_test(0.05,11.4,11.9,100,0.25)

II.4
t_test("sample1.txt",0.01,80)
t_test("sample1.txt",0.05,80)

II.5
z_test(0.01,49,52,64,sqrt(89.5))

II.6
z_test(0.05,30,29,40,sqrt(5))