A consumer wishes to estimate the proportion of processed food items that contain genetically modified (GM) products.

(a) If no preliminary study is available, how large a sample size is needed to be 99 percent confident the estimate is within 0.03 of p?

(b) In a preliminary study, 210 of 350 processed items contained GM products. Using this preliminary study, how large a sample size is needed to construct a 99% confidence interval within 0.03 of p?