1. Make a table of values and probabilities for the Wilcoxon signed rank statistic T+ for the case when n = 4, similar to what we did in class for n = 3. 2. Laureysens et al. (2004) measured metal content in the wood of 13 poplar clones growing in a polluted area, once in August and once in November. Concentrations of aluminum (in micrograms of Al per gram of wood) are shown below. Clone August November August-November Columbia River 18.3 12.7 -5.6 Fritzi Pauley 13.3 11.1 -2.2 Hazendans 16.5 15.3 -1.2 Primo 12.6 12.7 0.1 Raspalje 9.5 10.5 1.0 Hoogvorst 13.6 15.6 2.0 Balsam Spire 8.1 11.2 3.1 Gibecq 8.9 14.2 5.3 Beaupre 10.0 16.3 6.3 Unal 8.3 15.5 7.2 Trichobel 7.9 19.9 12.0 Gaver 8.1 20.4 12.3 Wolterson 13.4 36.8 23.4 There are two nominal variables: time of year (August or November) and poplar clone (Columbia River, Fritzi Pauley, etc.), and one measurement variable (micrograms of aluminum per gram of wood). The differences are somewhat skewed; the Wolterson clone, in particular, has a much larger difference than any other clone. Make a comparative boxplot of the concentraion of aluminum for the samples collected in August and in November. Analyze the data to see if there is a difference in the concentraion of aluminum in samples collected at different times of the year, using: a. paired t-test b. Wilcoxon signed-rank test c. a Fisher rank test d. permutation e. bootstrap