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
HCB are known as 0.40 and 1.00 (nanograms2 per liter), respectively. But the sample sizes and sample means are the same as the previous problem.
(a) Apply an appropriate procedure to determine if the data support the claim that the population means are the same.
(b) Suppose that the true difference in mean concentrations is 2.0 nanograms per liter. What is the power of the statistical test in part (a)?
(c) What sample size would be required to detect a difference of 1.0 nanograms per liter at ? = 0.05 if the power must be at least 0.9?