Polycyclic aromatic hydrocarbons (PAHs)-formed during the incomplete burning of oil, gas, or coal-are considered to be potential dangerous pollutants by the Environmental Protection Agency (EPA). Consider an actual developer who purchased a large parcel of land in Florida that he planned to turn into a residential community. Because the parcel turned out to have significant deposits of PAHs, the developer was required to remove these pollutants from the site prior to commencing development. The clean-up was completed, but the housing bubble burst and the development was a bust. The developer blamed the failure of his plan on the discovery of the pollutants, and filed suit against two industries (named Industry A and B) that were within 25 miles of the site. Although both industries produced PAH waste materials as part of their industrial processes, both denied responsibility for the pollution. Experts were hired to investigate the degree of similarity between pollutants at the industrial sites and those at the development site. Soil specimens were collected at each of four locations: 7 at the housing development site, 8 at Industry A, 5 at Industry B, and 2 at Industry C. Two different molecular diagnostic ratios for measuring the level of PAH in soil were determined for each soil specimen.

These data are displayed in the accompanying table.

a. A biochemical expert hired by Industry A chose to analyze the data using a series of t-tests for comparing two means. That is, he conducted a two-sample t-test (Section 8.2) using a = .05 for each possible pair of sites: Industry A vs. Industry B, Industry A vs. Industry C, Industry A vs. Development, Industry B vs. Industry C, Industry B vs. Development, and Industry C vs. Development. The results of these 6 t-tests for the second PAH ratio variable led the expert to conclude that (1) mean PAH2 ratio at the development site is statistically different from the corresponding mean at Industry A and (2) the mean PAH2 ratio at the development site is not statistically different from the corresponding mean at Industry B. Use the data in the PAH file to replicate these results.
b. The inferences derived in part a led the expert to argue that the source of the PAH contamination at the housing development site is more likely to have been derived from Industry A than from Industry B. A statistician, hired to rebut this testimony, argued that the analysis (and subsequent inference) was flawed. Explain why.
c. Propose a better, more statistically valid, method of analyzing the data. Conduct this analysis for both dependent variables, PAH Ratio 1 and PAH Ratio 2. What do you conclude?

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RATIO Soil Specimen SITE РАН1 РАН2 Development Development Development Development Development Development Development 0.620 1.040 2 0.630 1.020 0.660 1.070 4 0.670 1.180 0.610 1.020 6. 0.670 1.090 0.660 1.100 IndustryA IndustryA IndustryA IndustryA IndustryA IndustryA IndustryA IndustryA 0.620 0.950 0.660 0.700 0.560 1.090 10 0.960 0.970 11 12 0.560 1.000 13 0.570 1.030 14 15 0.600 0.970 0.580 1.015 1.130 1.110 16 IndustryB IndustryB IndustryB 0.770 17 0.720 18 0.560 0.980 0.705 0.670 19 20 1.130 1.140 IndustryB 21 IndustryC IndustryC 0.675 1.115 22 0.650 1.060