Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.

(a) Calculate a 95% two-sided confidence interval on the death rate from lung cancer.

(b) Using the point estimate of p obtained from the prelimi- nary sample, what sample size is needed to be 95% condi- dent that the error in estimating the true value of p is less than 0.03?

(c) How large must the sample be if we wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?