An article in the Journal of the Environmental Engineering Division (“Distribution of Toxic Substances in Rivers,” 1982, Vol. 108, pp. 639–649) investigates the concentration of several hydrophobic organic substances in the Wolf River in Tennessee. Measurements on hexachlorobenzene (HCB) in nanograms per liter were taken at different depth downstream of an abandoned dump site. Data for two depths follow:
Surface: 3.74, 4.61, 4.00, 4.67, 4.87, 5.12, 4.52, 5.29, 5.74, 5.48
Bottom: 5.44, 6.88, 5.37, 5.44, 5.03, 6.48, 3.89, 5.85, 6.85, 7.16
(a) What assumptions are required to test the claim that mean HCB concentration is the same at both depths? Check those assumptions for which you have the information.
(b) Apply an appropriate procedure to determine if the data support the claim in part a.
(c) Suppose that the true difference in mean concentrations is 2.0 nanograms per liter. For a = 0.05, what is the power of a statistical test for H0: μ1 = μ2 versus H1: μ1 = μ2?
(d) What sample size would be required to detect a difference of 1.0 nanograms per liter at a = 0.05 if the power must be at least 0.9?