Testing and Estimating m with s Known Let x be a random variable that represents micrograms of lead per liter of water (g/L). An industrial plant discharges water into a creek. The Environmental Protection Agency has studied the discharged water and found x to have a normal distribution, with s 5 0.7 g/L

(Reference: EPA Wetlands Case Studies).

(a) The industrial plant says that the population mean value of x is m 5 2.0 mg/L. However, a random sample of n 5 10 water samples showed that x 5 2.56 mg/L. Does this indicate that the lead-concentration population mean is higher than the industrial plant claims? Use a 5 1%.

(b) Find a 95% confi dence interval for m using the sample data and the EPA value for s.

(c) How large a sample should be taken to be 95%

confi dent that the sample mean x is within a margin of error E 5 0.2mg/L of the population mean?