Page 244 - Statistics for Environmental Engineers

L1592_frame_C27.fm Page 247 Tuesday, December 18, 2001 2:47 PM

Exercises
27.1 Recycled Water Irrigation. Evaluate an irrigation system that uses recycled water to grow cucum-
bers and eggplant. Some field test data are given in the table below. Irrigation water was applied
in two ways: sprinkle and drip. Evaluate the yield, yield per gallon, and biomass production

Irrigation Irrigation Yield Yield Biomass
2
Vegetable Type Source (lb/ft ) (lb/gal) (lb/plant)
Cucumber Sprinkle Tap water 6.6 0.15 5.5
Recycled water 6.6 0.15 5.7
Drip Tap water 4.9 0.25 4.5
Recycled water 4.8 0.25 4.0
Eggplant Sprinkle Tap water 2.9 0.07 3.0
Recycled water 3.2 0.07 3.5
Drip Tap water 1.6 0.08 1.9
Recycled water 2.3 0.12 2.3
27.2 Water Pipe Corrosion. Students at Tufts University collected the following data to investigate
the concentration of iron in drinking water as a means of inferring water pipe corrosion. (a)
Estimate the main effects and interactions of the age of building, type of building, and location.
(b) Make the normal plot to judge the significance of the estimated effects. (c) Based on duplicate
observations at each condition, the estimate of σ is 0.03. Use this value to calculate the variance
2
2
of the average and the main and interaction effects. Use Var y() = S p /N and Var(Effect) = 4S p /N ,
where N = total number of measurements (in this case N = 16) to evaluate the results. Compare
your conclusions regarding significance with those made using the normal plot.
Age Type Location Iron (mg/L)
Old Academic Medford 0.23 0.28
New Academic Medford 0.36 0.29
Old Residential Medford 0.03 0.06
New Residential Medford 0.05 0.02
Old Academic Somerville 0.08 0.05
New Academic Somerville 0.03 0.08
Old Residential Somerville 0.04 0.07
New Residential Somerville 0.02 0.06

27.3 Bacterial Tests. Analysts A and B each made bacterial tests on samples of sewage effluent
and water from a clean stream. The bacterial cultures were grown on two media: M1 and
M2. The experimental design is given below. Each test condition was run in triplicate. The
2
y values are logarithms of the measured bacterial populations. The s i are the variances of
the three replicates at each test condition. (a) Calculate the main and interaction effects using the
averages at each test condition. (b) Draw the normal plot to interpret the results.(c) Average
σ
σ
the eight variances to estimate σ for the experiment. Use Var y() = ------ 2 and Var(effect) = ------ 2
2
24 6
to evaluate the results. [Note that Var(effect) applies to main effects and interactions. These
variance equations account for the replication in the design.]
Source Analyst Medium y (3 Replicates) y i s i 2
Effluent A M1 3.54 3.79 3.40 3.58 0.0390
Stream A M1 1.85 1.76 1.72 1.78 0.0044
Effluent B M1 3.81 3.82 3.79 3.81 0.0002
Stream B M1 1.72 1.75 1.55 1.67 0.0116
Effluent A M2 3.63 3.67 3.71 3.67 0.0016
Stream A M2 1.60 1.74 1.72 1.69 0.0057
Effluent B M2 3.86 3.86 4.08 3.93 0.0161
Stream B M2 2.05 1.51 1.70 1.75 0.0750
© 2002 By CRC Press LLC