Question: Suppose we are planning a randomized trial of dietary interventions affecting weight gain in women. We want to compare women randomized to a high-fiber diet vs. women randomized to a low-fiber diet, with the outcome being 10+ lb weight gain after 5 years. We anticipate that after 5 years 20% of the women in the low-fiber group and 10% of the women in the high-fiber group will have gained 10+ lb.
(a) How many women need to be randomized in each group to achieve 80% power if a two-sided test will be used with a 5% significance level?
(b) Suppose we recruit 250 women in each group. How much power will the study have?