The expected value of a Bernoulli variable is just the probability of that variable being a 1/Yes/On etc. The pi is another way for representing the p or probability of a yes/1/etc.
Basically you are testing whether one is less than the other or not.
The first thing is to establish your test statistic and the distribution that its associated to before you can worry about p-values. (Hint: Can you for a 2-sample t-test for your hypotheses)?