Question

Listed below are amounts​ (in millions of​ dollars) collected from parking meters by a security service company(SSC) and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service​ company's employees? SCC: 1.4, 1.7, 1.5, 1.6, 1.6, 1.3, 1.5, 1.7, 1.4, 1.7 Other Companies: 1.9, 1.8, 1.5, 1.7, 1.6, 1.8, 1.7, 1.6, 1.8, 1.7 Find the coefficient of variation for each of the two​ samples, then compare the variation. ​(Round to one decimal place as​ needed.) Do the limited data listed here show evidence of stealing by the security service​ company's employees? Consider a difference of greater than​ 1% to be significant.

Answer 1

Case1: SCC:

Mean = = 15.4/10 =1.54

x	x -	(x - )2
1.4	- 0.14	0.0196
1.7	0.16	0.0256
1.5	- 0.04	0.0016
1.6	0.06	0.0036
1.6	0.06	0.0036
1.3	- 0.24	0.0576
1.5	- 0.04	0.0016
1.7	0.16	0.0256
1.4	- 0.14	0.0196
1.7	0.16	0.0256
Total =		0.184

Variance = s² = 0.184/9 = 0.0204

So,

Standard Deviation = s =

So,

Coefficient of Variation (CV) is given by:

%

Case 2: Other companies:

Mean = = 17.1/10 =1.71

x	x -	(x - )2
1.9	0.19	0.0361
1.8	0.09	0.0081
1.5	- 0.21	0.0441
1.7	- 0.01	0.0001
1.6	- 0.11	0.0121
1.8	0.09	0.0081
1.7	- 0.01	0.0001
1.6	- 0.11	0.0121
1.8	0.09	0.0081
1.7	- 0.01	0.0001
Total =		0.129

Variance = s² = 0.129/9 = 0.0143

So,

Standard Deviation = s =

So,

Coefficient of Variation (CV) is given by:

%

Difference in CV = 9.29 % - 7.00 % = 2.29 %

So,

the difference is significant.

So,

the limited data listed here show evidence of stealing by the security service company's employees.