Question

A claim is made that there is no correlation between comfort and price in luxury cars. A sample of 10 models of luxury cars were ranked according to their comfort levels and their prices. These ranks are given in the table below.

Model Comfort Price

A 9 10

B 3 9

C 2 7

D 7 1

E 5 3

F   1 6

G 8 8

H 10 5

I 6 2

J 4 4

Round your answers to 3 places after the decimal point, if necessary.

(a) Find the value of the (Spearman's) rank correlation coefficient test statistic.

(b) Find the critical values of (Spearman's) rank correlation coefficient if this test is conducted at the 0.02 significance level. Do not type " ± ± " in front of your answer (the ± ± is already given in front of the answer box below).

C. What is the correct conclusion of this test?

Answer 1

Let be the true value of the Spearman's rank correlation coefficient between comfort and price in luxury cars.

We want to test the claim that there is no correlation between comfort and price in luxury cars. the hypotheses are

a) Since the ranks are already given, we just need to get the difference d between the ranks

Model	Comfort rank	Price rank	d=(Comfort-Price)
A	9	10	-1
B	3	9	-6
C	2	7	-5
D	7	1	6
E	5	3	2
F	1	6	-5
G	8	8	0
H	10	5	5
I	6	2	4
J	4	4	0

Number of observations n=10

the rank-correlation coefficient is

ans: the value of the (Spearman's) rank correlation coefficient test statistic is -0.018

b) The number of observations is n=10. Using the table for Spearman's Rank correlation, we look at the row corresponding to n=10 and alpha=0.02 (The table may provide the area under both the tails=0.02 or area under one tail=0.01) and get 0.745 as the upper critical value and -0.745 as the lower critical value

ans:  the critical values are +- 0.745

C) We will reject the null hypothesis if the test statistics lies outside the interval -0.745 to +0.745

Here, the test statistics is -0.018 and it leis within the interval -0.745 to +0.745. Hence we do not reject the null hypothesis.

ans: We conclude that at 0.02 level of significance, there is no sufficient evidence to reject the claim that there is no correlation between comfort and price in luxury cars.

That is we conclude that there is no correlation between comfort and price in luxury cars.