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 34 12 40 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                                                           independentnot independent of industry.

Answer 1

Hypotheses are:

H0: Transportation mode is independent of industry.

Ha: Transportation mode is not independent of industry.

Followng table shows the row and column total:

	Air	Train	Truck	Total
Publishing	34	12	40	86
Computer Hardwares	5	6	24	35
Total	39	18	64	121

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	Air	Train	Truck	Total
Publishing	27.72	12.79	45.49	86
Computer Hardwares	11.28	5.21	18.51	35
Total	39	18	64	121

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
34	27.719	1.42
5	11.281	3.5
12	12.793	0.05
6	5.207	0.12
40	45.488	0.66
24	18.512	1.63
Total		7.38

Following is the test statistics:

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(3-1)=2

The p-value is: 0.0250

Conclusion: Since p-value is less than 0.05 so we reject the null hypothesis. That is we can conclude that transportation mode is not independent of industry..

Excel function used for p-value: "=CHIDIST(7.38, 2)"