Question

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 2 4 3 6 7 5 8 1 Per capita Income In $1000 19 17 18 14 12 13 15 16 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 volumex Rank of per capita income in $1000 y (b) What is the level of significance? State the null and alternate hypotheses. OHPs = 0; H,:P:<0 OH :P = 0; HP 7 0 HP >0; Hy: P = 0 HP, = 0; Hy: P, > 0 (c) Compute the sample test statistic. (Use 3 decimal places.) (d) Find the p-value interval of the sample test statistic. ---Select-- < P-value < --Select-->

Answer 1

		x-y=
x rank	y rank	d	d2
7	1	6	36
5	3	2	4
6	2	4	16
3	6	-3	9
2	8	-6	36
4	7	-3	9
1	5	-4	16
8	4	4	16
		∑d2	142

b)

level of signifciance =0.01

O Hgi P = 0; H,: P +0

c)

test statistic =

rs=1-6Σd2/(n(n2-1))=

-0.690

d)0.05 < p< 0.1

e)

At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

f)

Fail to reject the null hypothesis, there is insufficient evidence that a monotonic relationship exists between insu