Q1. Both diabetes and high cholesterol interact to increase the risk of heart disease. Changing diet

Q1. Both diabetes and high cholesterol interact to increase the risk of heart disease. Changing diet affects both blood sugar and cholesterol. To investigate how different diets used to control diabetes affects cardiovascular risk factors, Neal Barnard and colleagues compared the effects of a low-fat vegan with the diet recommended by the American Diabetic Association.What is the power of this study to detect a change in mean total cholesterol from 190 to 165 mg/dL with a sample size of 20 people on each diet with 95% confidence? Based on earlier experience, the standard deviation of total cholesterol in the population is about 35 mg/dL.How large a sample size would be necessary to increase the power of this study to detect a 25 mg/dL change in total cholesterol to 80%?What is the minimum detectable effect one could obtain with 20 people in each group and 80% power?