Question

#29

Is there a relation between murder and arson? A random sample of 15 Midwest cities (over 10,000 population) gave the following information about annual number of murder and arson cases. (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
Murder	11	18	14	15	13	10	9	8	12	6	17	22	20	21	24
Arson	37	73	79	18	29	43	31	24	12	14	133	139	47	98	138

Use a 1% level of significance to test the claim that there is a monotone-increasing relationship between the ranks of murder and arson.

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

City	Murder Rank x	Arson Rank y	d = x - y	d2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15				Σd2 =

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

Answer 1

a)

		x-y=
x rank	y rank	d	d2
11	9	2	4
5	6	-1	1
8	5	3	9
7	13	-6	36
9	11	-2	4
12	8	4	16
13	10	3	9
14	12	2	4
10	15	-5	25
15	14	1	1
6	3	3	9
2	1	1	1
4	7	-3	9
3	4	-1	1
1	2	-1	1
		∑d2	130

c)

test statistic =

rs=1-6Σd2/(n(n2-1))=

0.768