'I hope you will' only makes sense if it comes immediately after the statement that it refers to. For example, if your friend says 'I think I'll pass the test', you could respond, 'I hope you will.' In one side of a communication, like an email, it would only work if it were an echo of the previous sentence. For example 'I had a great time on the course. I hope you will, too.'

If someone said: I will do something .... You can agree with him and say: I hope you will

I hope you'll help me out with my coursework. I hope you'll be my friend. I hope you'll be satisfied with the meal I've cooked. I hope you'll marry me one day.