Question

A random sample of firms that relocated to Texas in the last three years is conducted. Based on the contingency table to the right, provide a test of whether the industry type and primary reason for relocation are statistically independent at a significance level of α=0.05.

	Industry
Primary Reason	Manufacturing	Retail	Tourism	Row Total
Technology	53	25	10	88
Tax Credits	67	36	20	123
Labor Force	30	40	33	103
Column Total	150	101	63	314

a. Calculated Chi-Squared statistic

b. Critical (upper) Chi-Square for α=5%

c. Conclusion for α=5%

Answer 1

Null hypothesis : H_o : Industry type and primary reason for relocation are statistically independent

Alternate Hypothesis : H_a : Industry type and primary reason for relocation are not statistically independent

a.

Test Statistic

O : Observed Frequency

E: Expected Frequency

Given,

O: Observed Frequency	Industry
Primary Reason	Manufacturing	Retail	Tourism	Row Total
Technology	53	25	10	88
Tax Credits	67	36	20	123
Labor Force	30	40	33	103
Column Total	150	101	63	314

E: Expected Count/Frequency	Manufacturing	Retail	Tourism
Technology	(88*150) / 314	(88*101) / 314	(88*63) / 314
Tax Credits	(123*150) / 314	(123*101) / 314	(123*63) / 314
Labor Force	(103*150) / 314	(103*101) / 314	(103*63) / 314

E: Expected Count/Frequency	Manufacturing	Retail	Tourism	Row total
Technology	42.0382	28.3057	17.6561	88
Tax Credits	58.7580	39.5637	24.6783	123
Labor Force	49.2038	33.1306	20.6656	103
Column Total	150	101	63	314

O	E	O-E	(O-E)2	(O-E)2/E
53	42.0382	10.9618	120.1607	2.8584
25	28.3057	-3.3057	10.9279	0.3861
10	17.6561	-7.6561	58.6151	3.3198
67	58.7580	8.2420	67.9312	1.1561
36	39.5637	-3.5637	12.6999	0.3210
20	24.6783	-4.6783	21.8869	0.8869
30	49.2038	-19.2038	368.7868	7.4951
40	33.1306	6.8694	47.1890	1.4243
33	20.6656	12.3344	152.1373	7.3619
			Total	25.2095

Test Statistic

b.

Degrees of freedom = (number of rows-1)*(number of columns -1) =(3-1)*(3-1) =4

Critical value of for =5%(0.05) for 4 degrees of freedom = 9.49

c.

As Value of the test statistic : 25.2095 > Critical value of :9.49; Reject the null hypothesis.

There is sufficient evidence to conclude that Industry type and primary reason for relocation are not statistically independent