There continue to be studies regarding the link between smoking and lung cancer. In the medical records for a simple random sample of 1000 deceased smokers and 1000 deceased nonsmokers, it was found that 126 of the smokers and 20 of the non smokers died of lung cancer related causes. 

a. Build and interpret the 95% confidence interval estimate of the difference in lung cancer caused mortality rates for the two populations represented here.

b. Suppose we wanted to ensure a margin of error for a 95% confidence interval estimate of the population difference that is no larger than 1% (that is, .01). How large a sample would you recommend? Assume sample sizes will be equal. Use the results of the original sample here as “pilot” study results.