How can I create a deep neural network which has a capability to take a decision for hypothesis?
If you are sure enough that the alternative hypothesis data come from different distribution than the null hypothesis, you can try unsupervised learning algorithm. i.e a K-mean or a GMM with the right number of cluster could yield a great separation of the data. You can then assign label to the second class data and train a classifier using it. 
This a general approach of semi-supervised learning.
Another idea would be to consider the alternative hypothesis data as outliers and use anomalie detection algorithm to find you second class data point. This is much more difficult to achieve and rely heavily on the supposition that data comes from really different distribution.
Basically, I am interested in solving a hypothesis problem, where I am only aware of the data distribution of a null hypothesis and don't know anything about the alternative case.
My concern is how should I train my deep neural network so that it can classify or recognise whether a particular sample data has a similar distribution as in null hypothesis case or it's from another class(An alternative Hypothesis case).
According to my understanding, It's different from a binary classification (one vs all case), because in that case, we know what data we are going to tackle, but here in my case alternative hypothesis case can follow any data distribution.
Here I am giving you an example situation, what I want exactly 

Suppose I want to predict that a person is likely to have cancer or not
e.g
I have a data set of the factors that cause cancer like, 
Parameter A=1,Parameter B=3.87,Parameter C=5.6,Has cancer = yes 
But I don't have a data set where 
Parameter A=2,Parameter B=1.87,Parameter C=2.6,Has cancer = No

Can be anything like this 
Means I don't know about anything which leads to a conclusion of not having cancer, can I still train my model to recognise whether a person has cancer?