Testing and Estimating μ, σ Known. Let x be a random variable which represents micorgrams of lead per liter of water (ug/l). An industrial plant discharges water in a creek. the Environmental Protection Agency has studied discharged water and found x to have normal distribution, with σ = 0.7 ug/l.
a) The industrial plant says that population mena value of x is μ= 2.0 ug/l. But, a random sample of n =10 water samples showed that x = 2.56 ug/l. Does this point that the lead concentration population mean is higher than the industrial plant claims? Use a 1%.
b) Find a 95% confidence interval for μ using 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 x is within a margin of error E= 0.2 ug/l of the population mean?