My girlfriend has recently gotten a job doing sales and trading at a major bank. Buoyed by her new job, she believes she can predict whether stocks will be up or down at the end of the month greater than chance (she believes she can even do it with 80% accuracy!)

I am very skeptical. We have agreed to do an experiment in which she will choose a number of stocks and, at a predetermined time, we will check if they are up or down.

My question is this: how many stocks would she have to pick, and how many would she have to get right, in order to have enough statistical power to tell with confidence that she can accurately predict stocks?

For example, how many stocks would she have to pick to tell with 95% certainty that she pick stocks with 80% accuracy?