1.You want to compare response rates (percent) of two regimens. A power of 90% and a two-sided test of size 0.05 are desired. How many patients are needed to detect a difference between true response rates of p₁=30% and p₂=50%? Let the proportion in group 1 be q₁ = 0.4. (2 points)

2.Two medications are being evaluated to determine their effects on the time it takes arthritis patients to walk 50 feet. Assume this time is normally distributed with standard deviation of 10 seconds for either treatment. In a randomized trial to compare treatments A and B, how many patients are needed to determine if one treatment is better than the other by an average of 10 seconds? Assume 90% power and alpha = 5% (two-sided). Let q₁ = q₂ = 0.5. (2 points)

3.The research question is whether % body fat and bone density in a selected group of adults are correlated. The investigator believes that those with a high percentage of body fat have a higher level of bone density. A previous study found a modest correlation (r = 0.2). How many individuals will need to be enrolled, at alpha (one-sided) = 0.05 and beta = 0.1? (2 points)

4.Suppose you are interested in measuring the mean cholesterol among a group of obese men with a 95% confidence interval of +/- 5. Assume a standard deviation of 20. Use the appropriate formula and derive the required sample size. (2 points)

1.96

5.The specificity of a given test is 90%. How many subjects are required to estimate a 99% confidence interval for the tests specificity of +/- 0.05? (2 points)