Contaminated water: 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. Assume that water samples are being drawn from a river in order to estimate the PCB concentration. Suppose that a random sample of size 60 has a sample mean of 1.96 parts per billion ( ppb). Assume the population standard deviation is . = 0.35 ppb.
a. Construct a 98% confidence interval for the PCB concentration.
b. EPA standards require that the PCB concentration in drinking water be no more than 0.5 ppb. Based on the confidence interval, is it reasonable to believe that this water meets the EPA standard for drinking water? Explain.
c. Estimate the sample size needed so that a 98% confidence interval will have a margin of error of 0.03.