Question

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 7 13 8 11 17 24 19 15 18 16 14 23 6 20 22 Arson 49 374 53 32 123 127 16 91 13 47 166 12 74 107 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. Murder Rank x Arson Ranky d = x-y d2 lyd- = (b) What is the level of significance? 0.01 State the null and alternate hypotheses. 0 1 : P < 0; H: P2 = 0 OH :P = 0; HP, + 0 Ho: Ps = 0; Hy: Ps > 0 O Hops = 0; H: P < 0 (c) Compute the sample test statistic. (Use 3 decimal places.) Enter a numhar

Answer 1

		x-y=
x rank	y rank	d	d2
14	8	6	36
11	10	1	1
13	15	-2	4
12	7	5	25
7	11	-4	16
1	3	-2	4
5	2	3	9
9	12	-3	9
6	5	1	1
8	13	-5	25
10	9	1	1
2	1	1	1
15	14	1	1
4	6	-2	4
3	4	-1	1
		∑d2	138

b) level of significance =0.01

. Ho: P = 0; H7: Ps > 0

c)

test statistic =

rs=1-6Σd2/(n(n2-1))=

0.754