 This is the example number four for two-sample hoteling t-square distribution. Two-sample hoteling t-square distribution and the example for the two-sample is the n1 equal to n2 equal to 50. We have 50 sample values. The following result we obtained like this. Here is the mean of the first sample and this is the mean of the second sample and this is the sample covariance metric 98 multiplied by s. This is the sample covariance metric where s is the pooled estimate of common variance covariance metric. 98 is the multiple of s. Now, we want to test at alpha 0.10 level and the hypothesis is two-sample hypothesis is mu1 equal to mu2. This is the two-tailed test. Now, the solution is, so we have, we know that total hypothesis testing k takes steps there. Now, the number one step construct the hypothesis. We have the null and alternative hypothesis. Second step is the level of significant. Here alpha equal to 10 percent. Third step is the test statistic. This is the test statistic of two-sample hoteling t-square. Now, the fourth step is the calculation. Fourth step is the calculation. This is the t-square. Now, the x1 minus x2. This is the x1, x2 and this x1 minus x2. Now, the s-invert. This is the s. Now, s multiplied by 98 times of s. Finally, we have calculated the value of s when we divide it. Okay, this is the s. Now, how much is the total dimension of s? We have the s of 4 cross 4. Now, we want the s-inverts. We want the 4 cross 4 of s-inverts. So, manually, it is possible that we take out s-inverts 4 cross 4. So, you can easily find the 4 cross 4 of s-inverts in Excel. We have already checked in Excel how to find the 3 cross 3 of s-inverts. Now, you can easily find the 4 cross 4 of s-inverts on Excel. After the value of s-inverts, finally, the t-square statistic is this. This is the mean x1 minus x2 prime. This is the s-inverts and this is the x1 minus x2. In the formula, you have t-square and you have n1n2 divided by n1 plus n2. Finally, the calculation is complete. After the calculation, the final result we have t-square which is equal to 2580.84. Now, the next step is the critical region. Here is the alpha by 2. This is the table value and p and p comma n1 plus n2 minus p minus 1. This is the degree of freedom. So, p, how many dimensions? We have 4 dimensions. So, n1 equal to 50, n2 equal to 50. We have entered its value. So, finally, we have alpha because alpha, you know that alpha which is equal to 0.10. Now, the alpha by 2 which is equal to 0.05. Finally, what happened? 4.95. Now, where is this value? This is the table value. Now, we have the table of alpha 0.05 for 4 and the 95. Here, we have somewhere 95 and we have the value 2.45. On which we have checked? For a particular example, we have taken the value of 120. What is the next value of 95? We have taken the value of 120. Last time, we have checked interpolation. In interpolation, you can interpolate it. This is the 2.45. We can also interpolate. We will easily find the value that you have. What value is determined on 4.95? Here, we have taken the value of 4 120 which is equal to 2.45. We multiply this factor and the final result is 10.109. If we round off it, it is 10.11. What was the calculated value? We had seen the calculated value in the previous example. 2580 which is greater than the table value. So, what is the conclusion? If the calculated value is greater than the table value, so we reject H0 at 10% level of significance. So, this is the example of the Hortling t-square for two samples.