** Testing and Estimating **m

**s**

*,***Let**

*Known**x*be a random variable that represents micrograms of lead per liter of water (ug/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 σ= 0.7ug/l

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

(b) Find a 95% confidence interval for μusing the sample data and the EPA value for σ.

(c) How large a sample should be taken to be 95% confident that the sample mean is within a margin of error *E *= 0.2 ug/l of the population mean?