1. Suppose we want to design a new placebo-controlled trial to evaluate an experimental medication to increase lung capacity. The primary outcome is peak expiratory flow rate, a continuous variable measured in liters per minute. The primary outcome will be measured after 6 months on treatment. The expected peak expiratory flow rate in adults is 300 with a standard deviation of 50. How many subjects should be enrolled to ensure 80% power to detect a difference of 15 liters per minute with a two sided test with ? = 0.05

2. An investigator wants to estimate caffeine consumption in high school students. How many students would be required to ensure that a 95% confidence interval estimate for the mean caffeine intake (measured in mg) is within 15 units of the true mean? Assume that the standard deviation in caffeine intake is 68 mg.

3. Consider the study proposed in problem #2. How many students would be required to estimate the proportion of students who consume coffee? Suppose we want the estimate to be within 5% of the true proportion with 95% confidence.

4. A clinical trial was conducted comparing a new compound designed to improve wound healing in trauma patients to a placebo. After treatment for 5 days, 58% of the patients taking the new compound had a substantial reduction in the size of their wound as compared to 44% in the placebo group. The trial failed to show significance. How many subjects would be required to detect the difference in proportions observed in the trial with 80% power? A two sided test is planned at ? = 0.05

5. A crossover trial is planned to evaluate the impact of an educational intervention program to reduce alcohol consumption in patients determined to be at risk for alcohol problems. The plan is to measure alcohol consumption (the number of drinks on a typical drinking day) before the intervention and then again after participants complete the educational intervention program. How many participants would be required to ensure that a 95% confidence interval for the mean difference in the number of drinks is within 2 drinks of the true mean? Assume that the standard deviation of the difference in the mean number of drinks is 6.7 drinks.

6. An investigator wants to design a study to estimate the difference in the proportions of men and women who develop early onset cardiovascular disease (defined as cardiovascular disease before age 50). A study conducted 10 years ago, found that 15% and 8% of men and women, respectively, developed early onset cardiovascular disease. How many men and women are needed to generate a 95% confidence interval estimate for the difference in proportions with a margin of error not exceeding 4%?

7. The mean body mass index (BMI) for boys age 12 is 23.6. An investigator wants to test if the BMI is higher in boys age 12 living in New York City. How many boys are needed to ensure that a two-sided test of hypothesis has 80% power to detect an increase in BMI of 2 units? Assume that the standard deviation in BMI is 5.7.

8. An investigator wants to design a study to estimate the difference in the mean BMI between boys and girls age 12 living in New York City. How many boys and girls are needed to ensure that a 95% confidence interval estimate for the difference in mean BMI between boys and girls has a margin of error not exceeding 2 units? Use the estimate of the variability in BMI from problem #7.