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 are shown below. (Reference: EPA Wetland Case Studies.)Reading 1 2 3 4 5 6 7 8 9 10 11 12Inlet (mg/l) 59.1 25.7 70.5 71.0 37.6 43.5 13.1 24.2 16.7 49.1 67.6 31.7Outlet (mg/l) 18.2 14.3 15.3 17.5 13.1 8.0 4.1 4.4 4.3 5.8 16.3 7.1Use a 1% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of the inlet readings and outlet readings.(a) 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.Reading InletRank x OuletRank y d = x - y d2123456789101112Σd2 =

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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 are shown below. (Reference: EPA Wetland Case Studies.)Reading        1        2        3        4        5        6        7        8        9        10        11        12Inlet (mg/l)        59.1        25.7        70.5        71.0        37.6        43.5        13.1        24.2        16.7        49.1        67.6        31.7Outlet (mg/l)        18.2        14.3        15.3        17.5        13.1        8.0        4.1        4.4        4.3        5.8        16.3        7.1Use a 1% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of the inlet readings and outlet readings.(a) 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.Reading        InletRank x        OuletRank y        d = x - y        d2123456789101112Σd2 =

Kristina Petty · Accepted Answer

r    s    =  1  −            6      ∑              d        2                    n      (              n        2            −      1      Spearman&#039;s correlation coefficient is given by the formula given above. Here n= 12Reading 1 2 3 4 5 6 7 8 9 10 11 12Inlet (mg/l) 59.1 25.7 70.5 71 37.6 43.5 13.1 24.2 16.7 49.1 67.6 31.7Outlet (mg/l) 18.2 14.3 15.3 17.5 13.1 8 4.1 4.4 4.3 5.8 16.3 7.1Inlet Rank X 9 4 11 12 6 7 1 3 2 8 10 5Outlet Rank Y 12 8 9 11 7 6 1 3 2 4 10 5d= x-y -3 -4 3 1 -1 1 0 0 0 4 0 0d^2 9 16 9 1 1 1 0 0 0 16 0 0         (   Summation d^2) = (9+16+9+1+1+1+16)= 53

Turbid water is muddy or cloudy water. Sunlight is necessary for most life forms; thus turbid water

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