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//Two-tailed Test Concerning Difference between Two Means
//(When the variances of the Populations are UnKnown and the Sample Sizes are Large)
//Example8.22
//page265
//Test : Ho:u1=u2 or u1-u2=0
// H1: u1#u2 or u1-u2#0
clc;
Sigma1 = input('Enter the variance of population1')
Sigma2 = input('Enter the varinace of population2')
n1 = input('Enter the sample size taken from population1')
n2 = input('Enter the sample size taken from population2')
X1 = input('Enter the mean of the sample1')
X2 = input('Enter the mean of the sample2')
alpha = input('Enter the significance level')
alpha = alpha/2;
//Calculation of Z statistic
Z_X1_X2 = Students_t_Var_Unknown(X1,X2,Sigma1,Sigma2,n1,n2)
disp(Z_X1_X2,'calculated Normal Z-statistic =')
Z_alpha = stand_students_t_VarUnkn(alpha)
disp(Z_alpha,'Standard Normal Stastistic=')
if ((-Z_alpha < Z_X1_X2) &(Z_X1_X2< Z_alpha)) then
disp('It falls in the Acceptance Region')
disp('Then Null Hypothesis Ho should be Accepted')
else
disp('It falls in the Rejection Region')
disp('Then Null Hypothesis Ho should be Rejected')
end
//Result
//Enter the variance of population1 2.5
//Enter the varinace of population2 4
//Enter the sample size taken from population1 16
//Enter the sample size taken from population2 20
//Enter the mean of the sample1 38.5
//Enter the mean of the sample2 40
//Enter the significance level 0.1
//Sp= 3.3382353
//Sigma= 0.6128225
//calculated Normal Z-statistic = - 2.4476906
//Standard Normal Stastistic= 1.645
//It falls in the Rejection Region
//Then Null Hypothesis Ho should be Rejected
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