Environmental Engineering Reference
In-Depth Information
a mean and standard deviation of 0.903 and
0.951, respectively. Evaluate whether the postde-
velopment distribution of concentrations is sig-
nificantly different from the predevelopment
distribution at the 10% significance level.
use the Mann-Kendall test to assess whether
there is a trend in the data at the 5% significance
level.
10.29.
use the concentration data given in Problem
10.28 along with Sen's slope estimator to esti-
mate the slope of the time series measurements
and the 90% confidence interval of the slope.
10.25.
Annual rainfall in the 20 years prior to 1970
show a mean of 1320 mm, and a standard devia-
tion of 250 mm, while data recorded during the
17 years after 1970 show a mean of 1450 mm and
a standard deviation of 220 mm. Does the data
support the hypothesis that all measurements
were drawn from a normal population with the
same mean and variance? use a 10% signifi-
cance level.
10.30.
Simultaneous measurements of two water-
quality variables,
X
and
Y
, are as follows:
x
y
x
y
x
y
x
y
35.72
60.57
41.66
59.29
47.33
57.57
53.39
57.37
36.32
57.01
42.95
55.77
48.62
61.57
54.59
58.81
37.25
59.08
43.85
60.97
49.51
62.96
55.99
60.13
10.26.
Concentration data are collected during differ-
ent periods in a water body. Each set of data has
25 samples and the measured concentrations
from each sample set are shown below:
38.60
56.95
44.92
67.67
50.15
63.43
56.53
59.81
39.75
60.03
45.78
58.42
51.23
59.02
-
-
40.27
59.37
46.60
60.38
52.72
61.43
-
-
Determine the correlation coefficient between
X
and
Y
, and assess whether there is significant
correlation at the 10% significance level.
Set1 Set2 Set1 Set2 Set1 Set2 Set1 Set2 Set1 Set2
0.18 2.11 0.94
1.02 3.28 1.06 5.07 2.24 1.23 10.28
3.90 2.70 1.88
1.42 7.82 1.07 4.98 0.50 1.95
2.59
10.31.
Water-quality variables,
X
and
Y
, are measured
simultaneously and the results are as follows:
1.70 5.45 0.96
0.84 2.46 2.22 0.49 1.86 0.46
8.56
1.01 1.31 0.33
4.49 8.20 3.81 1.46 1.13 2.25
2.26
0.51 0.34 3.76 38.00 1.24 1.84 9.10 0.64 3.45
0.68
x
y
x
y
x
y
x
y
34.77
66.96
40.95
68.92
46.91
72.75
52.81
74.16
use the Kruskal-Wallis test to determine
whether the population means from which the
data sets are drawn are significantly different at
the 10% level.
36.04
71.67
42.09
73.71
48.10
71.85
53.92
73.41
37.25
71.43
42.89
72.31
49.05
73.57
54.86
76.48
38.07
70.78
43.87
71.67
50.18
73.33
55.77
72.29
39.22
72.65
45.24
69.67
51.15
70.44
-
-
10.27.
Consider the random data given by:
40.03
70.79
45.77
71.61
52.01
74.02
-
-
Estimate the parameters of a linear equation
relating the two variables and the 90% confi-
dence intervals of the parameters.
10.32.
use the data and results in Problem 10.31 to
estimate the 90% confidence intervals of predic-
tions of
y
at
x
= 45 and
x
= 55. Compare the
width of these confidence intervals.
10.33.
Two sets of concentration measurements are to
be combined. The first set consists of 15 measure-
ments, assumed to be drawn from a population
distribution having a mean and standard devia-
tion of 1.26 and 0.89 mg/l, respectively. The
second set of 20 measurements is assumed to be
drawn from a population distribution with a
mean and standard deviation of 1.12 and
0.74 mg/l, respectively. Assuming that both sets
of measurements are independent of each other,
determine the mean and standard deviation of a
weighted average of these data.
1.333
1.295
1.109
−0.727
1.160
1.612
1.487
0.640
0.452
0.903
2.597
−0.352
0.144
2.960
2.308
1.073
0.398
0.662
−0.207
−0.807
Assess the normality of these random fluctua-
tions at the 5% significance level using the
Shapiro-Wilk test.
10.28.
Concentration measurements taken at annual
intervals at a particular location in a water body
are as follows:
year,
i
c
i
(mg/l)
year,
i
c
i
(mg/l)
1
38.46
6
56.59
2
46.34
7
38.90
3
51.34
8
47.89
4
54.65
9
53.95
5
56.74
10
51.11
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