Question

#33 Babita

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)	88.5	58.5	69.8	58.0	80.4	20.2	18.4	63.6	91.5	55.7	70.5	90.5
Outlet (mg/l)	9.9	4.2	13.4	5.8	9.4	4.8	3.2	10.5	16.1	3.5	7.6	14.5

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) From the given data

X	Y	Ranks of X	Ranks of Y	di = R(xi)-R(yi)	di^2
88.5	9.9	3	5	-2	4
58.5	4.2	8	10	-2	4
69.8	13.4	6	3	3	9
58	5.8	9	8	1	1
80.4	9.4	4	6	-2	4
20.2	4.8	11	9	2	4
18.4	3.2	12	12	0	0
63.6	10.5	7	4	3	9
91.5	16.1	1	1	0	0
55.7	3.5	10	11	-1	1
70.5	7.6	5	7	-2	4
90.5	14.5	2	2	0	0
				Total =	40

c) Test for correlation Coefficient :

Test Statistic t = 5.332