clear
X=[46 37 39 48 47 44 35 31 44 37];
Y=[35 33 31 34 34 30 27 32 31 31];

n1=length(X);
n2=length(Y);

alpha=0.05; # significance level


#The null hypothesis is: H0: vx!=vy (the standard is meet) (the variances differ)
#The alternative hypothesis is: H1: vx=vy (the standard is not meet) (the variances are the same)
#Both tail test when sigma is unknown


[H, PVAL, CI, STATS] = vartest2(X,Y,'alpha',alpha,'tail','both');

if H==1
  printf("The null hypothesis is rejected\n\n");
  printf("The data suggests that the standard is not meet\n\n");
  printf("The variances seem to be the same");
else
  printf("The null hypothesis is not rejected\n\n");
  printf("The data suggests that the standard is meet\n\n");
  printf("The variances seem to differ\n\n");
endif

z_alpha = norminv(alpha/2, 0, 1); # calculating tt of alpha/2

RR = [-inf z_alpha]; # first part of the regection region

z_alpha2 = norminv(1-alpha/2, 0, 1); # calculating tt of 1-alpha/2

RR2 = [z_alpha2 +inf]; # second part of the regection region

printf("The regection region is: (%4.3f, %4.3f) reunited with (%4.3f, %4.3f)\n",RR,RR2);
printf("The observed value of the test statistic is: %4.3f\n", STATS.fstat );
printf("The Pvalue of the test is: %4.3f\n\n",PVAL);

oneminualpha=0.95; # confidence level

a1= (mean(X) - mean(Y) - tinv(1-alpha/2,n1+n2-2)*sqrt(((n1-1)*var(X)+(n2-2)*var(Y))/(n1+n2-2))*sqrt(1/n1+1/n2));

a2=(mean(X) - mean(Y) + tinv(1-alpha/2,n1+n2-2)*sqrt(((n1-1)*var(X)+(n2-2)*var(Y))/(n1+n2-2))*sqrt(1/n1+1/n2));


printf("The Confidence interval between population means when sigma1=sigma2, where sigma and sigma2 are unknown, is (%4.3f, %4.3f)\n", a1,a2);