Question

1. Suppose we have the following values on the number of customers (X) and the average profits (Y) for fifteen stores:

Store                   Customers (X)            Average Profits (Y)

A                               161                              157

B                               99                              93

C                               135                              136

D                               120                              123

E                                164                              153

F                                221                              241

G                               179                              201

H                               204                              206

I                                 214                              229

J                                101                              135

K                               231                              224

L                                206                              195

M                               248                              242

N                               107                              115

O                               205                              197

Use the Spearman’s Rank Correlation test at the 0.05 level to see if X and Y are significantly related.

Answer 1

Solution:

The calculations for the spearsman rank correlation is given in the below table.

Store	Customers(X)	Rank(X)	Average profit(Y)	Rank(Y)	di =Rx - Ry	di^2
A	161	6	157	7	-1	1
B	99	1	93	1	0	0
C	135	5	136	5	0	0
D	120	4	123	3	1	1
E	164	7	153	6	1	1
F	221	13	241	14	-1	1
G	179	8	201	10	-2	4
H	204	9	206	11	-2	4
I	214	12	229	13	-1	1
J	101	2	135	4	-2	4
K	231	14	224	12	2	4
L	206	11	195	8	3	9
M	248	15	242	15	0	0
N	107	3	115	2	1	1
O	205	10	197	9	1	1
Total						32

Here, di is the difference between the rank X and rank Y.

The formula for the spearsman's correlation coefficient when there is no tied between the rank is given as,

We are testing,

The null hypothesis state the variable X and Y is not significant.

The alternative hypothesis state that variable X and Y are significant.

The P-value at r = 0.94286 and degree of freedom (n-1 = 13) is approx to 0 obtained by use of the online calculator.

Therefore, we reject the null hypothesis and conclude that the variable X and Y are significantly related.

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