Question

Question 1 Test, at the 5% level of significance, whether location (Parramatta or Sydney CBD) of the business is related to the type of business (privately held, publicly traded or franchise)?

Column 1 Profit What was your profit?

Column 2 Type Is the business privately held, publicly traded or a franchise? (Private = 1, Public = 2, Franchise = 3)

Column 3 Employee How many employees work at your business?

Column 4 Age How old is the company (in years)?

Column 5 Location Where is the company? (1 = Parramatta CBD, 2 = Sydney CBD)

(PLEASE ANSWER IN EXCEL)

3 1 3 1 1 1 1 1 1 2 3 3 2 1 2 1 1 3 1 3 1 1 1 1 1 3 1 Profit Type 173000 98000 130000 111000 22000 116000 109000 155000 77000 104000 151000 109000 65000 57000 119000 130000 159000 129000 173000 114000 108000 154000 78000 202000 100000 103000 147000 191000 47000 208000 78000 136000 17000 122000 104000 151000 84000 175000 18000 97000 66000 114000 136000 90000 88000 167000 75000 115000 101000 118000 161000 122000 159000 145000 141000 150000 86000 158000 53000 63000 133000 138000 141000 89000 135000 38000 166000 81000 118000 94000 1 1 2 1 2 3 1 2 1 1 1 3 1 3 1 1 2 2 1 Employ! Age 16 9 17 14 25 15 25 9 16 19 22 19 11 19 28 17 22 16 18 15 24 20 21 17 10 21 20 31 21 19 20 20 5 23 21 26 25 18 12 23 18 11 19 34 17 22 16 20 23 17 21 24 13 23 30 20 22 19 20 12 21 21 22 11 20 14 27 15 32 18 Locatio 8.6 10.5 14.2 11 8.8 10.7 113 15.6 10 14.2 8.7 8.5 14.4 9 15.1 11.7 11.4 12.1 14.7 12.9 10.4 10.5 15.2 9.5 9.6 7.7 10.4 9.1 8.9 18.3 10.7 15.4 6.9 9.4 17.6 11.5 15.2 10.7 6.6 9.7 12.4 14.3 9.6 13.4 14.6 9.6 7.9 20.3 16.3 9.1 16.5 8.9 11.1 14.1 16.1 13.9 13 9.7 11 9 15.6 12.2 14.5 14.7 15.7 9.8 8.5 10.5 10 8.9 1 1 2 1 1 1 1 2 1 2 z 2 1 1 1 1 2 2 2 2 1 1 2 2 1 1 2 1 1 2 1 2 1 1 1 1 2 1 1 1 2 2 1 2 2 1 1 2 1 1 2 1 1 2 1 1 2 1 2 1 1 2 2 2 3 2 2 1 1 1 1 2 2 2 3 1 3 1 2 3 1 2 2 1 1 1 1 3 1 1 1 2 2

Answer 1

Given information summarised into the contingency table as below,

We will use Chi-square test:

	Parramatta	Sydney	Total
Private	28	11	39
Public	7	9	16
Franchise	5	10	15
Total	40	30	70

$1590233366828_image.png$

To test the hypothesis is that the location of the business is related to the type of business at a 5% level of significance.

Hypothesis:

H0: The location of the business is not related to the type of business.

HA: The location of the business is related to the type of business.

$1590233375850_image.png$

Chi square test :

Oij= Observed frequencies

	Parramatta	Sydney	Total
Private	O11= 28	O12=11	R1=39
Public	O21=7	O22=9	R2=16
Franchise	O31=5	O32=10	R3=15
Total	C1=40	C2=30	N=70

Now we will calculate Expected frequencies as,

Eij (Ri * Cj) N

Therefore expected frequencies are

E11=(39*40)/70=22.286	E12=(39*30)/70=16.714
E21=(16*40)/70=9.143	E22=(16*30)/70=6.857
E31=(15*40)/70=8.571	E32=(15*30)/70=6.429

$1590233390553_image.png$

The Formula for Chi-square:

ChiSquare = x = [ (Oij – Eij)! Eij

$Chi Square = \chi ^2 =[(28-22.286)^2/22.286]+[(11-16.714)^2/16.714]$$+[(7-9.143)^2/9.143]+[(9-6.857)^2/6.857]+[(5-8.571)^2/8.571)]$$+[(10-6.429)^2/6.429]$

$\mathbf{Chi Square = \chi ^2 = 8.0629}$

$1590233400308_image.png$

Degrees of freedom:

Formula for Chi square Degrees of Freedom (df) is,

df = (R-1)(C-1) where, R = number of rows and C = number of columns

= (3 -1) * (2 - 1)

df = 2

$1590233402532_image.png$

P-Value:

P-value calculate using excel function =CHIDIST(8.0629,2)

Here,

8.0629 is a test statistic value

2 indicates degrees of freedom

therefor,

$\mathbf{P-Value=0.0177}$

$1590233406968_image.png$

Decision:

P-value(0.0177)<0.05 hence we reject H0

$1590233409713_image.png$

Conclusion:

P-value < 0.05 we reject H0, Hence we concluded that there is sufficient evidence to indicate that the location of the business is related to the type of business.