Use the Wilcoxon test to analyze the data given in Example 9.12. Example 9.12 Particulate matter from

Use the Wilcoxon test to analyze the data given in Example 9.12.

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Example 9.12 Particulate matter from roads contributes to pollution when those particles are washed into nearby waterways by rain. The size of the particles can impact the effectiveness of various stormwater control measures. The authors of the article "Characterizing Runoff from Roads: Particle Size Distributions, Nutrients, and Gross Solids" (J. Environ. Engr. 2016) took roadside measurements at several sites in North Carolina. For each assay they recorded d50, the median size of particles in the assay (a standard measure of particle size in such studies). Here are the d50 values (microns) for n = 9 assays performed off I-40 near Black Mountain: Previous studies indicated that the typical d50 value alongside roads of this type is 44 microns. Does the sample data provide convincing statistical evidence that the true mean d50 value differs from 44 microns? Let's carry out a test using a significance level of α = .01. 82.9 56.8 66.5 49.4 105.4 79.5 82.5 50.7 43.0 1. μ = true average d50 value (microns) for particulate matter assays at the Black Mountain site 2. Ho: μ = 44 H: μ + 44 3. A normal probability plot (not shown) indicates that the population distribution could plausibly be normal, so the one-sample t test will be used. x - 44 s/√√n 4. t = x - Ho s/√√n 5. From Appendix Table A.6, to/2n-1=1.005,8 = 3.355. So we reject Ho if either t > 3.355 or t≤ -3.355. 6. From the data provided, x = 68.52 and s= 20.49. Substituting, t= 68.52-44 24.52 20.49/√9 6.83 - = 3.59 7. Because the computed value t = 3.59 falls in the rejection region (3.59 3.355), Ho is rejected at the .01 level. Even this small sample of data provides convincing statistical evidence that the true mean d50 value for roadside particulates at the Black Mountain site differs from the "typical" value of 44 microns seen in other studies.