Environmental Engineering Reference
In-Depth Information
Estimate the mean, standard deviation, and
skewness of the population from which these
samples were drawn and assess the uncertainty
of the parameter estimates.
tively. Estimate the 90% confidence interval of
the standard deviation of the annual rainfall.
10.18.
Water-quality samples are collected at two
nearby locations in coastal waters. At one loca-
tion, 31 water-quality samples show that log-
transformed concentrations of a particular
substance have a standard deviation of 1.08, and
analysis of 21 samples at a second location show
a standard deviation of 1.53. Assuming that both
sets of data are drawn from log-normal distribu-
tions, determine the 90% confidence interval of
the ratio of the actual standard deviations.
10.10.
Consider the case where
N
random samples are
drawn from a Weibull distribution,
f
(
x
), which is
given by
a
a
b
a
b
−
f x
( )
=
x
a
−1
exp
,
x
≥
0
a
where
a
and
b
are the parameters of the distribu-
tion. Estimate the maximum likelihood values of
a
and
b
.
10.19.
A 20-year rainfall record prior to 1966 indicates
a variance of 239 cm
2
, and the 23-year record
after 1966 indicates a variance of 255 cm
2
. Esti-
mate the upper confidence limit of the 90% con-
fidence interval for the ratio of the post-1966 to
the pre-1966 variance.
10.11.
Assuming that the concentration data in Example
10.9 can be represented by a log-normal distribu-
tion, use the method of l-moments to estimate
the mean and standard deviation of the log-
normal distribution.
10.20.
Analysis of 41 log concentration measurements
show a sample mean of 0.523 and a sample stan-
dard deviation of 0.725. It is proposed that the
population mean is equal to 0.680. Would you
accept this hypothesis at the 10% significance
level?
10.12.
using the sample data given in Example 10.8,
calculate the expected values and the standard
errors of the mean, standard deviation, coeffi-
cient of skewness, median, and coefficient of
variation.
10.21.
Analysis of a 24-year record of mean monthly
flows in a river during the month of July indicates
that the mean and standard deviation are 42 and
8.1 m
3
is respectively. It is suggested that the pop-
ulation is normal with a mean of 38 m
3
/s, does the
data support this hypothesis? An alternate sug-
gestion is that the population is normally distrib-
uted with a mean greater than 45 m
3
/s. Does the
data support this hypothesis? Consider both
hypotheses at the 10% significance level.
10.13.
Based on 20 years of data, the average annual
rainfall in Everglades national Park is calculated
as 51 in, the standard deviation is estimated as
10.2 in, and the skewness is 0.3. What is the stan-
dard error in the mean, standard deviation, and
skewness of the annual rainfall?
10.14.
Analysis of the natural logarithms of 41 concen-
tration samples (in mg/l) show a mean and stan-
dard deviation of 0.893 and 0.786, respectively.
Determine the 90% confidence interval of the
population mean.
10.22.
Analysis of 41 log-concentration measurements
show a sample mean of 0.523 and a sample stan-
dard deviation of 0.725. It is proposed that the
population standard deviation is equal to 0.900.
Would you accept this hypothesis at the 10%
significance level?
10.15.
The mean and standard deviation of the annual
lake evaporation are calculated as 1160 and
221 mm, respectively. If these sample statistics
are derived from 24 years of data, what is the
90% confidence interval of the mean lake
evaporation?
10.23.
rainfall statistics derived from a 25-year record
yield a mean of 1201 mm and a standard devia-
tion of 125 mm. using a 10% significance level,
would you accept the hypothesis that the popula-
tion rainfall has a normal distribution with a
standard deviation of 100 mm?
10.16.
Analysis of the natural logarithms of 41 concen-
tration samples (in mg/l) show a mean and stan-
dard deviation of 0.893 and 0.786, respectively.
Determine the 90% confidence interval of the
population standard deviation.
10.24.
Before development around a lake, 21 water
samples showed the mean and standard devia-
tion of the log concentrations as 0.851 and 0.806,
respectively. After development, 21 samples have
10.17.
The mean and standard deviation of the annual
rainfall in a large catchment are estimated from
a 26-year record as 1520 and 389 mm, respec-
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