The body mass index is calculated by dividing a person's weight by the square of his or her height; it is a measure of the extent to which the individual is overweight. A researcher would like to test the hypothesis that men who develop diabetes have a higher BMI than men of similar age who do not. A literature review indicates that in healthy men, BMI is normally distributed, with a mean of 25 and a standard deviation of 2.7. The researcher proposes to measure 25 normal and 25 diabetic men. It is felt that a difference in average BMI of 2.7 (that is, one standard deviation) would be clinically meaningful. What is the power of the proposed study?