Suppose we are planning an exercise trial in 50–74-year-old men identifi ed as at high risk of a heart attack, to see if a daily exercise regime for a year will lead to a reduction in the number of heart attacks. One group will be given the daily exercise regime and the other control group will receive no help. On the basis of published evidence we expect that in the control group 20% of the men will have suffered a heart attack within the year.

We would be interested in detecting a reduction of heart attacks to 15%

in the exercise group. How many patients would be needed for a two-sided signifi cance of 5% and 80% power?