Determining the null hypothesis and its effect.

Hi, I still don't understand the concept of determining the null hypothesis and its effect on the calculation. In the video I linked below there is the following exercise: "Ajax releases a new dish detergent, called Extreme Ajax+, which they advertise to be able to clean many more dishes with a single bottle." Then you say that H0: μExtremeAjax+ - μAjax ≤ 0. What if Ajax claimed that Ajax+ did not work? In this case the data set would be the same but we have a different conlusion? It does not make sense to me. Then H0 would be: μExtremeAjax+ - μAjax > 0? No matter what the null hypothesis is I got a P value of 0.00964. The problem is that in the first case we reject the null hypothesis and say that Ajax+ is better, and in the second case we also reject the null hypothesis, but in this case it means that Ajax+ is not working, in spite of the fact that the data set is exactly the same so we got a paradox.  So my question is the following: If the H0 is the opposite (because Ajax says an opposite claim), do we get a different P-value? Does the null hypothesis have any effect on our calculation, and if yes, how because I got the same P-value?  Thanks in advance :). GB