Over the course of a year, a researcher took water samples from three areas in a forest with a stream running through it. Each sample was analyzed for the concentration of dissolved organic carbon (mg/L), with the results presented in the following table.

Each sample was categorized according to the water type collected. Water was collected from streams (surface water), groundwater was collected from organic soil, and groundwater was collected from mineral soil. The researcher wanted to determine if the distributions of concentration of dissolved organic carbon were the same for each collection area.
(a) State the null and alternative hypotheses.
(b) The sums of the ranks in each category are as follows:

Use this information to compute the test statistic.
(c) What is the critical value at the α = 0.05 level of significance?
(d) State your conclusion.
(e) Draw side-by-side boxplots to support your conclusion.

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Organic 22.74 6.51 9.72 17.90 11.40 16.87 14.90 14.00 8.81 18.30 7.40 5.30 15.42 29.80 14.86 19.80 27.10 5.29 15.91 5.20 17.50 14.86 15.72 22.49 16.51 15.35 20.46 20.46 8.09 11.90 10.30 Mineral 8.50 10.30 5.50 8.05 3.02 21.40 16.92 9.10 7.85 12.89 4.71 10.72 7.45 7.00 7.66 21.82 11.33 3.91 11.56 8.37 4.60 7.90 9.11 9.81 7.92 8.50 11.72 9.29 21.00 8.79 3.99 11.72 22.62 7.11 17.90 7.11 4,80 4.85 9.60 10.89 3.79 11.80 10.74 17.99 4.90 11.97 12.57 7.31