Chi-Square Test for Dependency between Company Location and Decision to Operate in UK
Added on 2023-05-29
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STATISTICS
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Question 1
Survey data to represents the companies based on which are operated on routes into or not into
the UK is highlighted below.
(a) Whether company operates into the UK and the country in which the company is based
would be determined through Chi- square test.
Null hypothesis H0: There is no dependency between the country of origin and the decision to
operate in UK or not.
Alternative hypothesis H1: There is dependency between the country of origin and the decision to
operate in UK or not.
Observed frequencies
France Italy
Into UK 102+43+29= 174 151+61+35= 247
Not into UK 56+66+38= 160 90+108+56 = 254
Expected frequencies
Expected frequencies
Country
France Italy Totals
Operate
d on
routes
Into UK =(421/835)*334 = 168.4000 =(421/835)*501 =252.6000 421
1
Survey data to represents the companies based on which are operated on routes into or not into
the UK is highlighted below.
(a) Whether company operates into the UK and the country in which the company is based
would be determined through Chi- square test.
Null hypothesis H0: There is no dependency between the country of origin and the decision to
operate in UK or not.
Alternative hypothesis H1: There is dependency between the country of origin and the decision to
operate in UK or not.
Observed frequencies
France Italy
Into UK 102+43+29= 174 151+61+35= 247
Not into UK 56+66+38= 160 90+108+56 = 254
Expected frequencies
Expected frequencies
Country
France Italy Totals
Operate
d on
routes
Into UK =(421/835)*334 = 168.4000 =(421/835)*501 =252.6000 421
1
Not into UK =(414/835)*334 = 165.6000 =(414/835)*501 = 248.4000 414
Totals 334 501 835
Chi- square calculation
Chi-square calculations
Country
France Italy
Operated
on routes
Into UK =(168.4-174)^2 /168.4 = 0.1862 =(252.6-247)^2/252.6= 0.1241
Not into UK =(165.6-160)^2 /165.6 = 0.1894 =(248.4-254)^2/248.4= 0.1262
Chi square statistic
X2 =0.1862+0.1241+0.1894+ 0.1262=0.6260
Degree of freedom = (r-1) (c-1) = (2-1)*(2-1) = 1
The corresponding p value = 0.428
Assuming a level of significance of 5%, it can be said that p value is higher than 5% and hence,
null hypothesis would not be rejected. It can be concluded that the decision to operate the
company in UK or not is not dependent on the country in which the company is based. It is
noteworthy that data on some additional nations would be required as France and Italy can both
show similar pattern especially considering the similar region and historical background.
(b) Whether company operates into the UK and the country in which the company is based Italy
would be determined through Chi- square test.
Null hypothesis H0: There is no dependency between the size of companies and the decision to
operate in UK or not for Italian companies.
Alternative hypothesis H1: There is dependency between the size of companies and the decision
to operate in UK or not for Italian companies.
2
Totals 334 501 835
Chi- square calculation
Chi-square calculations
Country
France Italy
Operated
on routes
Into UK =(168.4-174)^2 /168.4 = 0.1862 =(252.6-247)^2/252.6= 0.1241
Not into UK =(165.6-160)^2 /165.6 = 0.1894 =(248.4-254)^2/248.4= 0.1262
Chi square statistic
X2 =0.1862+0.1241+0.1894+ 0.1262=0.6260
Degree of freedom = (r-1) (c-1) = (2-1)*(2-1) = 1
The corresponding p value = 0.428
Assuming a level of significance of 5%, it can be said that p value is higher than 5% and hence,
null hypothesis would not be rejected. It can be concluded that the decision to operate the
company in UK or not is not dependent on the country in which the company is based. It is
noteworthy that data on some additional nations would be required as France and Italy can both
show similar pattern especially considering the similar region and historical background.
(b) Whether company operates into the UK and the country in which the company is based Italy
would be determined through Chi- square test.
Null hypothesis H0: There is no dependency between the size of companies and the decision to
operate in UK or not for Italian companies.
Alternative hypothesis H1: There is dependency between the size of companies and the decision
to operate in UK or not for Italian companies.
2
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