This is statistics for biology majors.

Women between ages 40 and 59 have a mean daily energy intake of 1800 kcal from foods and beverages. An investigator interviewed 16 women in this age range who led physically active lives. The sample mean daily energy intake of these women was 1720 kcal, with a sample standard deviation of 190 kcal. Now, the investigator plans a larger study of the association between physical activity and energy intake. The study will recruit two independent samples of women between ages 40 and 59. The first sample will consist of physically active women (different from those in problem 2); the second sample will consist of women with sedentary lifestyles. The null hypothesis will be that the true mean daily energy intakes of the two populations are equal; the alternative hypothesis is that they are not equal. The significance level of the test will be = .05.

1. Suppose that (1) the true mean daily energy intake of the physically active population is 1720 kcal, (2) the true mean daily energy intake of the sedentary population is 1800 kcal, and (3) the true standard deviation of daily energy intake in each population is 190 kcal. What will be the power of the hypothesis test if 36 women per group are recruited for the study?
2. Under the same assumptions as in part (a), how many women per group (assuming equal sample sizes) must be recruited for the hypothesis test to have 80% power?