The National Weight Control Registry tries to mine secrets of success from people who lost at least 30 pounds and kept it off for at least a year. It reports that out of 2,720 registrants, 439 were on...

The National Weight Control Registry tries to mine secrets of success
from people who lost at least 30 pounds and kept it off for at least a year.
It reports that out of 2,720 registrants, 439 were on a low-carbohydrate diet (less than 90 grams a day).

a. Develop a 95% confidence interval for the proportion of
people on a low-carbohydrate diet.

b. Is it possible that the population percentage is 16%?

c. How large a sample is needed to estimate the proportion
within 0.55%?