In an investigational study, researchers at Health-Wise Pharmaceuticals were treating benign tumors with repeated dosages of vitamin E. According to a pilot study, 30 out of 36 patients responded favorably to these treatments with shrunken tumors. How many patients must be sampled in a follow-up study to be 99% confident that the estimate will be within 0.125 of the true population proportion for those who respond favorably to the treatments?

According to prior published research, the amount of time a medical doctor spends with patients has a population standard deviation of 7.2 minutes. Further study is needed to estimate the true mean time medical doctors spend with their patients. If a researcher wants to be 96% confident that the estimate is within 2.4 minutes of the population parameter, what is the minimum sample size necessary for such findings?

The county council on healthy nutrition wants to estimate the amount of fat, in grams, that a typical fast food meal contains. The population range is known to be 144 grams, so the population standard deviation can be estimated with the Range Rule. How many samples must the council collect in order to be 99% confident that their estimate will be within the error or bound of four grams of the actual (population) mean fat content for these meals?