Statistics for Environmental Engineers

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40-49.9


1


0.007


0.986


50-59.9


1


0.007


0.993


60-69.9


0


0.000


0.993


70-79.9


1


0.007


1.000

Source: Prof. David Jenkins, University of California-Berkeley.


15.4 Rankit Regression. The table below gives eight ranked observations of a lognormally distributed variable y, the log-transformed values x, and their rankits.


(a) Make conventional probability plots of the x and y values. (b) Make plots of x and y versus the rankits. (c) Estimate the mean and standard deviation. ND = not detected (<MDL).


y    ND    ND 11.6    19.4    22.9    24.6    26.8    119.4


x = ln(y)    —    —    2.451    2.965    3.131    3.203    3.288    4.782


Rankit    -1.424    -0.852    -0.473    -0.153    0.153    0.473    0.852    1.424


15.5 Cohen’s Method—Normal. Use Cohen’s method to estimate the mean and standard deviation of the n = 26 observations that have been censored at yc = 7.


ND    ND    ND    ND    ND    ND    ND    ND    7.8    8.9    7.7    9.6    8.7


8.0    8.5    9.2    7.4    7.3    8.3    7.2    7.5    9.4    7.6    8.1    7.9    10.1


15.6 Cohen’s Method—Lognormal. Use Cohen’s method to estimate the mean and standard deviation of the following lognormally distributed data, which has been censored at 10 mg/L.


14    15    16 ND 72 ND 12 ND ND 20    52    16    25    33 ND 62


15.7 PCB in Sludge. Seven of the sixteen measurements of PCB in a biological sludge are below the MDL of 5 mg/kg. Do the data appear better described by a normal or lognormal distribution? Use Cohen’s method to obtain MLE estimates of the population mean and standard deviation.


ND ND ND ND ND ND ND 6    10    12    16    16    17


19    37    41

16

Comparing a Mean with a Standard


KEY WORDS t-test, hypothesis test, confidence interval, dissolved oxygen, standard.

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