The National Weight Control Registry tries to mine secrets of success from people who have lost at least 30 pounds and kept it off for at least a year. It reports that out of 2,700 registrants, 459 were on low-carbohydrate diets (less than 90 grams a day).
a. Develop a 95% confidence interval for this fraction.
b. Is it possible that the population percentage is 18%?
c. How large a sample is needed to estimate the proportion within 0.5%?