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 23 10 21 17 22 7 6 9 8 20 18 12 19 11 13 Arson 104 37 121 111 174 26 18 6 13 163 71 66 87 135 93 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 = (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)

Using rank order 1 as the largest data value

Here is the table of ranks

spearman rank correlation is

= 1- (6*122 / 15*(225-1) )

= 0.7821

b)

Level of significance is 0.01

Hypothesis

null hypothesis

alternate hypothesis

c)

Test statistic is

Here

r = Spearman rank correlation = 0.7821

= 4.5252