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? Write down methods that can be used to check those assumptions under the given the information. Each assumption should be checked by at least one method. And you are not required to describe the methods. Just write down the names and the sources where you found the methods.
(b) To test the claim in part (a), we may first want to decide whether the variances are equal. And unless some strong evidence persuade us the variances are equal, we tend to use the hypothesis testing with unequal variances. So please check whether the variances of two depths are equal under a "strict" standard, say ? = 0.20.
(c) According to your conclusion in part (b), apply an appropriate procedure to determine if the data support the claim in part (a).