z_test = function(n, sampleMean,pop_mean, stDev, alfa, type)
{
  if(type==0)
  {critical_z= qnorm(alfa);}
  else
  {if(type==1)
      {critical_z = qnorm(1-alfa);}
  else
  {critical_z= qnorm(1-alfa/2);}
  }
  z_score= (sampleMean - pop_mean)/ (stDev/ sqrt(n));
  if(type==0 && z_score< critical_z)
    {print(z_score); print(critical_z); print("The null hypothesis is rejected");return(0)}

  if(type==1 && z_score > critical_z)
    {print(z_score); print(critical_z); print("The null hypothesis is rejected"); return(0);}
  if(z_score != critical_z && type==2)
      {print(z_score); print(critical_z); print("The null hypothesis is rejected"); return(0);}
  print(z_score); print(critical_z); print("The null hypothesis holds");
  return(1);

}

#z_test(200, 816, 810, 50,0.05,1);

#Ex2
#z_test(49, 88,90, 12, 0.01,0)
#z_test(49, 88,90, 12, 0.05,0)

#Ex4
#z_test(100, 20.5, 21, 2.5, 0.01,0)

T_test_file = function(fileName, pop_mean,alfa, type)
{
  x= scan(fileName);
  if(type==0)
  {critical_t= qt(alfa,length(x)-1);}
  else
  {if(type==1)
  {critical_t = qt(1-alfa, length(x)-1);}
    else
    {critical_t= qt(1-alfa/2, length(x)-1);}
  }

  s= sd(x);
  se = s/sqrt(length(x));
  t_score = (mean(x) - pop_mean)/se;
  if(type==0 && t_score< critical_t)
  {print(t_score); print(critical_t); print("The null hypothesis is rejected");return(0)}

  if(type==1 && t_score > critical_t)
  {print(t_score); print(critical_t); print("The null hypothesis is rejected"); return(0);}
  if(t_score != critical_t && type==2)
  {print(t_score); print(critical_t); print("The null hypothesis is rejected"); return(0);}
  print(t_score); print(critical_t); print("The null hypothesis holds");
  return(1);

}

#T_test_file("program.txt",40, 0.05, 1)

T_test = function(x,pop_mean,alfa, type )
{
  if(type==0)
  {critical_t= qt(alfa,length(x)-1);}
  else
  {if(type==1)
  {critical_t = qt(1-alfa, length(x)-1);}
    else
    {critical_t= qt(1-alfa/2, length(x)-1);}
  }
  s= sd(x);
  se = s/sqrt(length(x));
  t_score = (mean(x) - pop_mean)/se;
  if(type==0 && t_score< critical_t)
  {print(t_score); print(critical_t); print("The null hypothesis is rejected");return(0)}

  if(type==1 && t_score > critical_t)
  {print(t_score); print(critical_t); print("The null hypothesis is rejected"); return(0);}
  if(t_score != critical_t && type==2)
  {print(t_score); print(critical_t); print("The null hypothesis is rejected"); return(0);}
  print(t_score); print(critical_t); print("The null hypothesis holds");
  return(1);

}
 #Ex2
#x= c(36, 32, 28, 33, 41, 28, 31, 26, 29, 34);
#T_test(x,34, 0.01, 2)
#Ex4
#T_test_file("history.txt", 80,0.01,2)


z_tests_mean = function (n1,n2, m0, mean1, mean2, stDev1, stDev2,alfa,type)
{
  if(type==0)
  {critical_z= qnorm(alfa);}
  else
  {if(type==1)
  {critical_z = qnorm(1-alfa);}
    else
    {critical_z= qnorm(1-alfa/2);}
  }
  combined_sigma = sqrt(stDev1^2/n1+ stDev2^2/n2);
  z_score = (mean1-mean2 -m0)/combined_sigma;
  if(type==0 && z_score< critical_z)
  {print(z_score); print(critical_z); print("The null hypothesis is rejected");return(0)}

  if(type==1 && z_score > critical_z)
  {print(z_score); print(critical_z); print("The null hypothesis is rejected"); return(0);}
  if(z_score != critical_z && type==2)
  {print(z_score); print(critical_z); print("The null hypothesis is rejected"); return(0);}
  print(z_score); print(critical_z); print("The null hypothesis holds");
  return(1);

}

#z_tests_mean(100,100, 0, 48,47,4,3,0.05,2)


#Ex2
#z_tests_mean(80,70,0,160,155,3.24,2.55,0.01,2)

#Ex3
#z_tests_mean(100,100,0, 22.8,23.3,1.3,1.9,0.01,2)

F_test_file = function(fileName, alfa, type)
{
  x1 = read.table("programm.txt", header = TRUE)[['A']];
  x2 = read.table("programm.txt", header = TRUE)[['B']];
  mean1= mean(x1);
  mean2= mean(x2);
  n1= length(x1);
  n2= length(x2);
  s1= sd(x1);
  s2= sd(x2);
  if(type==0)
    critical_f= qf(1-alfa,n1-1,n2-1);
  if(type==1)
    {critical_f_left = qf(alfa/2,n1-1,n2-1); critical_f_right = qf(1-alfa/2,n1-1,n2-1);}
  f_score= s1^2 / s2^2;
  if(type==0 && f_score>critical_f)
  {print(f_score); print(critical_f); print("Null hyp rejected"); return(0);}
  if(type==1 &&( f_score <critical_f_left || f_score > critical_f_right))
  {print(f_score); print(critical_f_left); print(critical_f_right); print("Null hyp rejected"); return(0);}
   print("Null hyp holds");
  return(1);
}

#ex2
#F_test_file("programm.txt",0.05,1)
#F_test_file("mice.txt",0.01,1)