Environmental Sampling Design - Fundamentals of Environmental Sampling and Analysis - page 66

17. A pigment manufacturing process has been generating waste over a number of years.
The wastes were discharged into a 40-acre lagoon. The pigment is generated in large
batches that involve a 24-h cycle: 16 h of high percentage of large-sized black particulate
matter and 8 h of smaller white pigment particles that are much smaller, settle more
slowly and travel further toward the effluent pipe. The lagoon has a distinct color strata,
with the black and the gray sludge each covering a quadrant measuring 1320 ft by 330 ft,
and the white sludge covering the remaining area of the lagoon, which measured 1320 ft
by 660 ft. The leachable contaminant (barium) was assumed to be associated with the
black sludge, which was concentrated in the first quadrant. The sludge had settled to a
uniform thickness throughout the lagoon and was covered with 2 ft of water. Design a
sampling plan (locations) using stratified random sampling. Assume that we need to
collect a total of 10 samples from the black sludge area (heavily contaminated), 10
samples from the gray area (mixed, less contaminated), and 20 samples from the large
strata (least contaminated).

1320 ft

Black sludge 330 ft

330 ft

Grey sludge

660 ft

White sludge

Overflow pipe

18. Thermal stratification is common in lakes located in climates with distinct warm and
cold seasons. It divides lakes into three zones (top: epilimnion; middle: thermocline;
bottom: hypolimnion). Because of the stratification, the vertical mixing of water is
prohibited. A stratified random sampling is designed to collect water samples for
nitrogen concentrations. The following data were obtained:

Volume Number of Nitrogen

Stratum (10 6 gal) samples taken concentration (mg/L)

Epilimnon (0-8 ft) 5 8 8, 6, 11, 16, 9, 17, 4, 13

Thermocline (8-10 ft) 1 2 11, 16

Hypolimnion (10-25 ft) 14 10 25, 17, 18, 11, 12, 10,

22, 16, 10, 11

(a) One of the objectives was to estimate the mean, standard deviation, and confidence
interval of the entire lake based on this stratified random sampling plan. Use 80%
confidence level.
(b) If the above nitrogen concentrations were obtained from simple random sampling
(i.e., total number of samples¼8þ2þ10 ¼ 20), calculate the mean, standard
deviation, and confidence interval at a 80% of confidence level.