Testing and Estimating μ, σ Known. Let x be the random variable which represents micorgrams of lead per liter of the water (ug/l). An industrial plant discharges water in 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 mean 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 out that the lead concentration population mean is higher than industrial plant claims? Employ a 1%.
b) Determine a 95% confidence interval for μ using sample data and EPA value for σ.
c) How large sample must be taken to be 95% confident that sample mean x is in a margin of error E= 0.2 ug/l of population mean?