daasda

#I.2 sim
#I.3
#I.3 as st
#N1=N2=100;X1=22.8;X2=23.3;S1=1.3;S2=1.9
#Inferenta asupra mediei - Testul Z pentru diferenta mediilor unor populatii
#cu dispersii cunoscute
zTestMeans=function (n1,x1,sigma1,n2,x2,sigma2,alfa,type)
{
  scorZ=(x1-x2)/sqrt((sigma1^2/n1)+(sigma2^2/n2));
  print(scorZ);
  if(type==-1)
  {
    critZ=qnorm(alfa,0,1);
    print(critZ);
    if(scorZ<critZ)
      print("Ipoteza nula este respinsa")
    else
      print("Se accepta ipoteza alternativa")
  }

  if(type==0)
  {
    critZ=qnorm(1-alfa/2,0,1);
    print(critZ);
    if(abs(scorZ)>abs(critZ))
      print("Ipoteza nula este respinsa")
    else
      print("Se accepta ipoteza alternativa")
  }
  if(type==1)
  {
    critZ=qnorm(1-alfa,0,1)
    if(scorZ>critZ)
      print("Ipoteza nula este respinsa")
    else
      print("Se accepta ipoteza alternativa")
  }
}
#I.3
zTestMeans(100,22.8,1.3,100,23.3,1.9,0.01,-1)

#I.2
zTestMeans(80,160,3.24,70,155,2.25,0.01,0)

#I.4

zTestMeans(100,3,0.6,100,3.5,0.4,0.01,-1)
zTestMeans(100,3,0.6,100,3.5,0.4,0.05,-1)

#I.5

zTestMeans(155,15,0.75,150,14.5,0.78,0.01,0)
zTestMeans(155,15,0.75,150,14.5,0.78,0.05,0)

#Inferenta asupra dispersiilor a doua populatii - Testul F
#II.2
f_test=function(alfa, n1,n2,s1,s2)
{
  critical_f_s=qf(alfa/2,n1-1,n2-1)
  critical_f_d=qf(1-alfa/2,n2-1,n1-1)
  f_score=s1/s2
  print(critical_f_s)
  print(critical_f_d)
  print(f_score)
  if( (f_score>=critical_f_s) && (f_score<=critical_f_d))
  {
    cat("Nu se respinge ipoteza nula")
  }
  else
  {
    cat("Ipoteza este respinsa")
  }
}
x1=read.table("program",header=TRUE, fill=TRUE)[['A']]
x2=read.table("program",header=TRUE, fill=TRUE)[['B']]
x1=x1[!is.na(x1)]
x2=x2[!is.na(x2)]
n1=length(x1)
n2=length(x2)
s1=sd(x1)*sd(x1)
s2=sd(x2)*sd(x2)
f_test(0.01,n1,n2,s1,s2)
f_test(0.05,n1,n2,s1,s2)

#II.3
f_test=function(alfa, n1,n2,s1,s2)
{
  critical_f_s=qf(alfa/2,n1-1,n2-1)
  critical_f_d=qf(1-alfa/2,n2-1,n1-1)
  f_score=s1/s2
  print(critical_f_s)
  print(critical_f_d)
  print(f_score)
  if( (f_score>=critical_f_s) && (f_score<=critical_f_d))
  {
    cat("Nu se respinge ipoteza nula")
  }
  else
  {
    cat("Ipoteza este respinsa")
  }
}
x1=read.table("program",header=TRUE, fill=TRUE)[['A']]
x2=read.table("program",header=TRUE, fill=TRUE)[['B']]
x1=x1[!is.na(x1)]
x2=x2[!is.na(x2)]
n1=length(x1)
n2=length(x2)
s1=sd(x1)*sd(x1)
s2=sd(x2)*sd(x2)
f_test(0.01,n1,n2,s1,s2)
f_test(0.05,n1,n2,s1,s2)

#TESTUL F DOAR CAZUL SIMETRIC


#Inferenta asupra mediilor a doua populatii - Testul T pentru diferenta medi-
 # ilor unor populatii cu dispersii necunoscute
#III.2

t_test_means=function(alfa,n1,n2,s1,s2,mean1,mean2)
{
  s1=s1*s1
  s2=s2*s2
  critical_f_s=qf(alfa/2,n1-1,n2-1)
  critical_f_d=qf(1-alfa/2,n2-1,n1-1)
  f_score=s1/s2
  if(f_score>=critical_f_s && f_score<=critical_f_d){
    df=n1+n2-2
    s=((n1-1)*s1+(n2-1)*s2)/df
    combined_s=sqrt(s/n1+s/n2)
  }else{
    df=min(n1-1,n2-1)
    combined_s=sqrt(s1/n1+s2/n2)
  }
  critical_t=qt(1-alfa/2,df)
  t_score=(mean1-mean2)/combined_s
  print(critical_t)
  print(t_score)

  if(abs(critical_t)>abs(t_score))
    print("Se accepta ipoteza nula")
  else
    print("se respinge ipoteza nula")
}
x1=read.table("program.txt",header=TRUE, fill=TRUE)[['A']]
x2=read.table("program.txt",header=TRUE, fill=TRUE)[['B']]
x1=x1[!is.na(x1)]
x2=x2[!is.na(x2)]
n1=length(x1)
n2=length(x2)
s1=sd(x1)
s2=sd(x2)
mean1=mean(x1)
mean2=mean(x2)
t_test_means(0.01,n1,n2,s1,s2,mean1,mean2)
t_test_means(0.05,n1,n2,s1,s2,mean1,mean2)


#III.3


t_test_means=function(alfa,n1,n2,s1,s2,mean1,mean2)
{
  s1=s1*s1
  s2=s2*s2
  critical_f_s=qf(alfa/2,n1-1,n2-1)
  critical_f_d=qf(1-alfa/2,n2-1,n1-1)
  f_score=s1/s2
  if(f_score>=critical_f_s && f_score<=critical_f_d){
    df=n1+n2-2
    s=((n1-1)*s1+(n2-1)*s2)/df
    combined_s=sqrt(s/n1+s/n2)
  }else{
    df=min(n1-1,n2-1)
    combined_s=sqrt(s1/n1+s2/n2)
  }
  critical_t=qt(1-alfa/2,df)
  t_score=(mean1-mean2)/combined_s
  print(critical_t)
  print(t_score)

  if(abs(critical_t)<abs(t_score))
    print("Se accepta ipoteza nula")
  else
    print("se respinge ipoteza nula")
}
x1=c(12.512,12.869,19.098,15.350,13.297,15.589)
x2=c(11.074,9.686,12.164,8.351,12.182,11.489)
n1=length(x1)
n2=length(x2)
s1=sd(x1)
s2=sd(x2)
mean1=mean(x1)
mean2=mean(x2)
t_test_means(0.01,n1,n2,s1,s2,mean1,mean2)