Question

Is the transportation mode used to ship goods independent of type of industry? Suppose the following contingency table represents frequency counts of types of transportation used by the publishing and the computer hardware industries. Analyze the data by using the chi-square test of independence to determine whether type of industry is independent of transportation mode. Let α = 0.05.

Transportation Mode

Industry

	Air	Train	Truck
Publishing	33	12	36
Computer Hardware	5	6	24

(Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.)

Observed χ2 =  
Transportation mode is (not independent OR independent) of industry.

Answer 1

Applying chi square test of independence:

Observed		Air	train	Truck	Total
	Publishing	33	12	36	81
	Computer Harfware	5	6	24	35
	total	38	18	60	116
Expected	Ei=row total*column total/grand total	Air	train	Truck	Total
	Publishing	26.53	12.57	41.90	81
	Computer Harfware	11.47	5.43	18.10	35
	total	38	18	60	116
chi square    χ2	=(Oi-Ei)2/Ei	Air	train	Truck	Total
	Publishing	1.58	0.03	0.83	2.4400
	Computer Harfware	3.65	0.06	1.92	5.6300
	total	5.2300	0.0900	2.7500	8.0700
Observed test statistic X2=		8.070

p value =

0.018

from excel: chidist(8.07,2)

since p value is less than significance level , we reject null hypothesis

Transportation mode is not independent of industry.