How many women need to be studied in each group (equal sample size per group) to have an 80% probability of detecting a significant difference if a two-sided test is used with a type I error of 5%?

Cancer

The effect of using postmenopausal hormones (PMH) on health outcomes is controversial. Most previous data collected have been from observational studies, and users of PMH may selectively differ from nonusers in ways that are difficult to quantify (e.g., more health conscious, more physician visits in which disease outcomes can be identified). A clinical trial was planned to randomize postmenopausal women to either PMH use or no PMH use and follow them for disease outcomes over a 10-year period. One outcome of special interest was breast cancer.

Suppose the incidence rate of breast cancer among postmenopausal 50-year-old women who do not use PMH is 200 per 105 women per year. Suppose also it is hypothesized that PMH increases the incidence of breast cancer by 20%.