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  = 0.05.

	Transportation Mode
Industry	Air Train Truck Publishing 32 12 36 Computer Hardware 5 6 24

Observed  =   
Transportation mode is                                                           independentnot independent of industry.

Answer 1

hypothesis:-

necessary calculation table:-

industries		transportation mode			row total
		air	train	truck
publishing	observed freq(Oi)	32	12	36	80
	expected freq (Ei)	(37*80)/112 = 26.4286	10.7143	42.8571
		1.1745	0.1543	1.0971
computer hardware	observed freq(Oi)	5	3	24	32
	expected freq (Ei​​​​​​​)	10.5714	4.2857	17.1429
		2.9363	0.3857	2.7429
column total		37	15	60	112

the test statistic be:-

degrees of freedom = (2-1)*(3-1) = 2

p value = 0.01433

in any blank cell of excel type =CHISQ.DIST.RT(8.4908,2) press enter]

decision:-

p value = 0.01433 < 0.05 (alpha)

so, we reject the null hypothesis.

conclusion:-

there is sufficient evidence to conclude that Transportation mode is not independent of industry at 0.05 level of significance.

*** if you have any doubt regarding the problem please write it in the comment box.if you are satisfied please give me a LIKE if possible..