Question

Is there a relation between police protection and fire protection? A random sample of large population areas gave the following information about the number of local police and the number of local fire-fighters (units in thousands). (Reference: Statistical Abstract of the United States.)

Area	1	2	3	4	5	6	7	8	9	10	11	12	13
Police	10.4	16.3	16.7	16.9	17.9	3.8	15.0	12.5	17.4	11.8	6.7	5.0	4.7
Firefighters	1.7	4.0	4.8	4.5	3.5	1.2	2.5	1.8	3.3	2.9	2.2	2.4	0.8

Use a 5% level of significance to test the claim that there is a monotone relationship (either way) between the ranks of number of police and number of firefighters.

(a) Rank-order police using 1 as the largest data value. Also rank-order firefighters using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test.

Area	Police Rank x	Firefighters Rank y	d = x - y	d2
1 2 3 4 5 6 7 8 9 10 11 12 13				Σd2 =

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

Answer 1