The National Center for Health Statistics interviewed 5409 adult smokers in 2015 , and 2636 of them said they had tried to quit smoking during the past year. Consider this to be a random sample.

a. Find a 95\% confidence interval for the proportion of smokers who have tried to quit within the past year.

b. Find a \(99 \%\) confidence interval for the proportion of smokers who have tried to quit within the past year.

c. Someone claims that the proportion is less than 0.5 . With what level of confidence can this statement be made?

d. Find the sample size necessary for a 95\% confidence interval to specify the proportion to within \(\pm 0.01\).

e. Find the sample size necessary for a \(99 \%\) confidence interval to specify the proportion to within \(\pm 0.01\).