Polychlorinated biphenyls (PCBs) are a group of synthetic oil-like chemicals that were at one time widely used as insulation in electrical equipment and were discharged into rivers. They were discovered to be a health hazard and were banned in the 1970s. Since then, much effort has gone into monitoring PCB concentrations in waterways. Assume that water samples are being drawn from a waterway in order to estimate the PCB concentration.

a. Suppose that a random sample of size 80 has a sample mean of 1.69 ppb and a sample standard deviation of 0.25 ppb. Find a 95% confidence interval for the PCB concentration.

b. Estimate the sample size needed so that a 95% confidence interval will specify the population mean to within ± 0.02 ppb.