1. "If we want to cut the maximum likely error in half, we'll have to double the sample size." Is this statement correct? Why or why not?

2. In determining the necessary sample size in making an interval estimate for a population mean, it is necessary to first make an estimate of the population standard deviation. On what bases might such an estimate be made?

3. From past experience, a package-filling machine has been found to have a process standard deviation of 0.65 ounces of product weight. A simple random sample is to be selected from the machine's output for the purpose of determining the average weight of prod- uct being packed by the machine. For 95% confidence that the sample mean will not differ from the actual population mean by more than 0.1 ounces, what sample size is required?

4. Based on a pilot study, the population standard deviation of scores for U.S. high school graduates taking a new version of an aptitude test has been esti- mated as 3.7 points. If a larger study is to be under- taken, how large a simple random sample will be nec- essary to have 99% confidence that the sample mean will not differ from the actual population mean by more  than  1.0 point?