Statistical Applications for Environmental Analysis and Risk Assessment

Answers for Exercises

Chapter 4

4.1. (v). 4.2. (iii). 4.3. Data are normally distributed. 4.4. The probability plot and Shapiro–Wilk test both indicate that the data are normal. 4.5. No. The RLs are probably too low to make a difference either way.

Chapter 5

5.1. (d). 5.2. (a). 5. 3. (iii). 5.4. (A) Year 6 PCB data are normally distributed. Year 1 PCB data also are somewhat normal, but the probability plot shows deviations from a linear pattern in the upper and lower tails (i.e., the presence of large and small values); (B) The quantile–quantile plot suggests that the two data populations have roughly similar distributions, but the Year 1 PCB values are higher than the Year 6 values, while the side-by-side box plots show that the mean and median PCB for Year 1are larger than for Year 6; (C) The double quantile plot shows that the Year 1 PCBs are higher than the Year 6 values, for both the center and the tail portions of the distributions; (D) There is a downward trend in the PCB concentrations.

Chapter 6

6.1. (v). 6.2. (a). 6.3. (d). 6.4. Original data are right-skewed, with outliers, while the log-transformed data are normal (meaning the data are lognormally distributed), with no outliers. (A) Mean; (B) For the original data, the 25% trimmed mean of 16.6 is approximately equal to the median of 16; (C) The logarithms are normally distributed and the outliers “disappear.” 6.5. The normal distribution fits the data better than the lognormal, but the reported value of 3.37 for ...