Question

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	12
Inlet (mg/l)	9.0	55.1	26.2	11.4	16.0	64.5	22.0	57.9	37.9	37.2	29.6	37.3
Outlet (mg/l)	2.7	15.2	3.4	2.6	3.8	18.8	3.5	17.3	15.8	9.8	14.0	13.8

Use 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	Inlet Rank x	Oulet Rank y	d = x - y	d2
1 2 3 4 5 6 7 8 9 10 11 12

Σd² =

(c) Compute the sample test statistic. (Use 3 decimal places.)

Answer 1

(a) Outlet Reading Inlet X d = | | | 8| ਗਗ p| 107 11 | 1 Cd =18 (c)

R. =-bgd nen 6(18) 12-12 =1 - 108 1716 =1-0.063 = 0.937

t=?:Vn-2 (0.937) V12-2 V1-(0.937) _2.963 0.349 = 8.490 The value of the sample test statistic is t = 8.490.