Question

#34

Big Rock Insurance Company did a study of per capita income and volume of insurance sales in eight Midwest cities. The volume of sales in each city was ranked, with 1 being the largest volume. The per capita income was rounded to the nearest thousand dollars.

Reading	1	2	3	4	5	6	7	8
Rank of insurance sales volume	6	8	4	1	3	2	5	7
Per capita income in $1000	16	13	17	19	18	15	12	14

Using a 0.01 level of significance, test the claim that there is a monotone relation (either way) between rank of sales volume and rank of per capita income.

(a) Using a rank of 1 for the highest per capita income, make a table of ranks to be used for a Spearman rank correlation test.

City	Rank of insurance sales volume x	Rank of per capita income in $1000 y	d = x - y	d2
1 2 3 4 5 6 7 8				Σd2 =

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

Answer 1

a)

		x-y=
x rank	y rank	d	d2
3	4	-1	1
1	7	-6	36
5	3	2	4
8	1	7	49
6	2	4	16
7	5	2	4
4	8	-4	16
2	6	-4	16
		∑d2	142

b)

level of significance =0.01

null hypothesis:		ps	=	0
Alternate Hypothesis:		ps	≠	0

c)

test statistic =

rs=1-6Σd2/(n(n2-1))=

-0.690

d) 0.05 < p value <0.10

e) fail to reject the null,,,,data are not statistically significant