Environmental Engineering Reference
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comparison, you need to anti-log the mean and median calculated after log transforma-
tion)? What conclusion can be drawn regarding the effect of logarithmic transformation
on the values of mean and median?
16. Soil samples were collected at two areas surrounding an abandoned mine and analyzed
for lead. At each area several samples were taken. The soil was extracted with acid, and
the extract was analyzed using flame atomic absorption spectrometry. In Area A, Pb
concentrations were 1.2, 1.0, 0.9, 1.4 mg/kg. In Area B, Pb concentrations were 0.7, 1.0,
0.5, 0.6, 0.4 mg/kg. (a) Are these two areas significantly different from each other with
Pb concentrations at 90% confidence level? (b) Perform a Single Factor ANOVA test
(i.e., One-Way ANOVA) using Excel.
17. Samples of bird eggs were analyzed for DDT residues. The samples were collected from
two different habitats. The data reported are:
Sample collection
Number of
Mean conc.
Standard
area
samples
DDT (ppb)
deviation (s)
Area 1
4
1.2
0.33
Area 2
6
1.8
0.12
(a) Are the two habitats significantly different (a¼5%) from each other in the amount
of DDT to which these birds are exposed?
(b) Calculate the 90% Confidence Intervals for DDT concentration in both areas.
(c) If DDT concentration in Area 2 can be assumed to have a normal distribution
with the same mean and standard deviation as the sample measurement listed in the
above table (i.e., m¼1.8 ppb, s¼0.12 ppb), what is the probability of a bird egg
having residual DDT of greater than 2.2 ppb? less than 2.2 ppb? or between 1.3 and
2.2 ppb?
18. PCB concentrations in fish tissues in two rivers have been determined (Data source:
Kebbekus and Mitra 1998). In River A the concentrations (mg/kg) were as follows: 2.34,
2.66, 1.99, 1.91 (Mean¼2.225, s¼0.3449); in River B (mg/kg): 1.55, 1.82, 1.34, 1,88
(Mean¼1.648, s¼0.2502). Determine the statistical significance for the concentration
difference between the two rivers (a 90% confidence level assumed).
19. The U.S. EPA wishes to test whether the mean amount of Radium-226 in a soil exceeds
the maximum allowable amount, 4 pCi/kg. (a) Formulate the appropriate null and
alternative hypotheses, (b) Describe a Type I error and a Type II error.
20. The following calibration data were obtained for a total organic carbon analyzer (TOC)
measuring TOC in water:
Concentration,
Number of
Mean signal
Standard
mg/L
replicates
(mv)
deviation
0.0
20
0.03
0.008
6.0
10
0.45
0.0084
10.0
7
0.71
0.0072
19.0
5
1.28
0.015
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