Question

Is there a relation between incidents of child abuse and number of runaway children? A random sample of cities (over 10,000 population) gave the following information about the number of reported incidents of child abuse and the number of runaway children. (Reference: Federal Bureau of Investigation, U.S. Department of Justice.) City 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Abuse cases 31 36 77 78 73 57 35 108 81 11 111 24 34 20 16 Runaways 536 312 690 567 442 649 293 550 755 184 668 380 318 297 278 Use a 1% level of significance to test the claim that there is a monotone-increasing relationship between the ranks of incidents of abuse and number of runaway children. (a) Rank-order abuse using 1 as the largest data value. Also rank-order runaways using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test. City Abuse Cases Rank x Runaways Rank y d = x - y d2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Incorrect: Your answer is incorrect. Incorrect: Your answer is incorrect. Σd2 = (b) What is the level of significance? Correct: Your answer is correct. State the null and alternate hypotheses. Ho: ρs > 0; H1: ρs = 0 Ho: ρs = 0; H1: ρs ≠ 0 Ho: ρs = 0; H1: ρs > 0 Ho: ρs = 0; H1: ρs < 0 Correct: Your answer is correct. (c) Compute the sample test statistic. (Use 3 decimal places.)

Answer 1

a)

s.no		Abuses cases		Runway					Abuses cases Rank x	Runway Rank y	d x-y	d²
1		31		536					11	7	4	16
2		36		312					8	11	-3	9
3		77		690					5	2	3	9
4		78		567					4	5	-1	1
5		73		442					6	8	-2	2
6		57		649					7	4	3	9
7		35		293					9	13	-4	16
8		108		550					2	6	-4	16
9		81		755					3	1	2	4
10		11		184					15	15	0	0
11		111		668					1	3	-2	4
12		24		380					12	9	3	9
13		34		318					10	10	0	0
14		20		297					13	12	1	1
15		16		278					14	14	0	0
											Total	96

b) ρs = 0; H1: ρs ≠ 0

c)

= 1 - 6(96)/(15³-15) = 1- 0.17142 = 0.828

sample test statistic rho =0.828