15b If you increase the number of patients to 100, how powerful would this test be?

The z-score will not change, but, because the standard error is much smaller, we will get a larger cut-off value.

This time, when we add the cut-off value to our truth curve, it goes to the right of the new mean (because 208 is a higher number than 205).

We again solve for z, then use the z to find the probability.

By increasing the sample size to 100, we would discover that our treatment is effect 82% of the time when it, in fact, is effect. Still, 18% of the time, we would fail to discover the effectiveness of the treatment.