I am doing a problem of hypothesis contrast and I have left the following results for the variable $X$ and $Y$ both normally distributed variables. For several sections I have obtained the following results
- For $\mu_X = 5$ -- I can not refuse this hypothesis
- For $\mu_Y = 4.6$ -- I can not reject this hypothesis
- For $\mu_X - \mu_Y <0.15$ -- I can not reject this hypothesis.
The difference between $\mu_X - \mu_Y = 0.4$ and in the third tells me that it is less than 0,15 so I do not know if it is due to the normal deviation (that I don't know) of the normal distribution or it is for another reason.
Then also another question: can it be the case to obtain a p-value equal to $0$?