Turbid water is muddy or cloudy water. Sunlight is necessary for most life forms; thus turbid water is considered a threat to wetland ecosystems. Passive filtration systems are commonly used to reduce turbidity in wetlands. Suspended solids are measured in mg/L. Is there a relation between input and output turbidity for a passive filtration system and, if so, is it statistically significant? At a wetlands environment in Illinois, the inlet and outlet turbidity of a passive filtration system have been measured. A random sample of measurements follow.

(i) Rank-order the inlet readings using 1 as the largest data value. Also rank-order the outlet readings using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test.
(ii) Use a 1% level of significance to test the claim that there is a monotone relation ship (either way) between the ranks of the inlet readings and outlet readings.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Compute the sample test statistic.
(c) Find or estimate the P-value of the sample test statistic.
(d) Conclude the test.
(e) Interpret the conclusion in the context of the application.

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Reading 1 2 3 45 6 78 9 10 12 Inlet (mg/L) 8.0 7.1 24.2 47.7 50.1 63.9 66.0 15.1 37.2 93.1 53.7 73.3 Outlet (mg/L) 2.4 3.6 4.5 14.9 7.4 7.4 6.7 3.6 5.9 8.2 6.2 18.1