I have a doubt about the theory of matched pair t-test. I have the difference between two means and I wanna do an hyphothesis-test analysis. I have the difference-mean, the difference-standard deviation and the degree of freedom.

Let’s start that I wanna say that the difference is equal to 0. So my null-hypotheses says that the difference is equal to 0. The alternative hypothesis says no. It’s a two tail problem. The significance level is set to 0.05 (alfa).

So, happens that if P-value is greater than alfa then I cannot reject the null hypothesis. If P-value is less than alfa then I reject the null hypothesis. This is clear!

Now, I wanna say that the difference is greater equal than D. The alternative hypothesis says that the difference is less than D (One tail problem). The significance level is set again to 0.05.

So, happens like before. Looking at the P-value I can/cannot reject the null hypothesis.

My doubts comes out now. I have made some tests and I see that for less value of D I get rejected the null hypothesis. Increasing D, I’m increasing the P-value. The fact is that if I continue to increase D for very big values, I will always be able to NOT reject the null hyphotesis! Doesn’t exist a D value big enough to reject the null hypothesis!

I’m guessing that I use the one problem tail just to find the lower/upper limit where I can not reject the null hypothesis! Is this correct or I wrote something wrong in my explanation?

Thanks!

Solimyr