Suppose you are proposing to test for a difference in mean outcome among two groups. A difference in mean of 10 units is hypothesized, compared to a null value of zero. The standard deviation of the outcome in both groups is 20 units. If you design a study to have simple random samples of the same numbers of observations from both groups, how large does each group need to be for the study to have 80% power, testing at the default = 0.05 level? How does the sample size change if the standard deviation was 40 units?