zconfidence_interval = function(n, sample_mean, alfa, deviation)
{
  sigma = sqrt(deviation);
  critical_z= qnorm(1-alfa/2,0,1);
  a= sample_mean-critical_z*sigma/sqrt(n);
  b = sample_mean+critical_z*sigma/sqrt(n);
  interval = c(a,b);
  return(interval)
}

#print(zconfidence_interval(8, 140,0.05,100))

test_proportion = function(n, alfa, succeses, p0, type)
{
  p_prim = succeses/n;
  if(type == 0)
  {critical_z=qnorm(alfa,0,1);}
  else {
    if(type == 1)
    {critical_z=qnorm(1-alfa,0,1);}
    else
    {if (type==2)
      critical_z=qnorm(1-alfa/2,0,1);
    }
  }
  z_score=(p_prim- p0)/sqrt(p0*(1-p0)/n);
  if(p_prim<p0 && z_score<critical_z)
    return ("First statement is false");
  if(p_prim>p0 && z_score> critical_z)
    return("First statement is false");
  if(p_prim != p0 && abs(z_score) > abs(critical_z))
    return("First statement is false");
  return ("First statement is true");
}
print(test_proportion(100, 0.01,48,0.509,0))
print(test_proportion(100, 0.05,48,0.509,0))