Question

Conception about the hypothesis test.

Question: can the data be test by poission distribution

H0: it can be test by poission

H1: it cant be test by poission model

Final: we fail to reject H0.

My Question: My prof told me that even though we fail to reject H0, but it doesnt mean that H0 is trues.

therefore, what should I write on my conclusion. should I write "yes, it can be test by poission model???"

However, it doesn't mean it is true

Please follow the comment

Answer 1

It is conceptually right to say that even if we fail to reject H0, it does not mean H0 is true. It is in the context that, we analyze only a sample data (portion of population) and this sample data may or may not provide convincing evidenc to reject the H0. It is possible that in one sample we may fail to reject the H0 while in other sample we get the evidence to reject H0. Despite all this fact, when it comes to reporting of conclusion we conclude only on the basis of the evidence available from our analysis of sample data with a level of certainity which is generally called level of significance.

Now, we come to your problem, your final result is "we fail to reject the H0" that means you do not have enough evidene against H0 to reject it on the basis of your analysis. Hence, you can conclude that "Yes , it can be test by Poisson distribution". You do not to mention anything else about it.

I hope I have made it clear, If you have any doubt, please ask in comments.