1. Assume 50 random samples of the same sample size are taken from a population, and a 90% confidence interval is constructed from each sample. How many of the intervals would you expect to contain the true population mean?
2. The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today's sample contains 14 defectives. How many units would have to be sampled to be 95% confident that you can estimate the fraction of defective parts within 2% (using the information from today's sample--that is using the result that p^=0.0875)?