Question

QUESTION:

The 2012 Restaurant Industry Forecast takes a closer look at today’s consumers. Based on a 2011 National Restaurant Association survey, American adults are categorized into one of three consumer segments (Optimistic, Cautious, and Hunkered down) based on their financial situation, current spending behavior, and economic outlook, as well as the geographic region where they reside. Suppose the results, based on a sample 1000 American adults, are as follows:

ORIGINAL DATA

	MIDWEST	NORTHEAST	SOUTH	WEST	TOTAL
OPTOMISTIC	67	23	60	63	213
CAUTIOUS	101	57	127	133	418
HUNKERED DOWN	83	46	115	125	369
TOTAL	251	126	302	321	1000

EXPECTED FREQUENCY TABLE

	MIDWEST	NORTHEAST	SOUTH	WEST
OPTOMISTIC	53.463	26.838	64.326	68.373
CAUTIOUS	104.918	52.668	126.236	134.178
HUNKERED DOWN	92.619	46.494	111.438	118.449

FINAL TABLE

	MIDWEST	NORTHEAST	SOUTH	WEST
OPTOMISTIC	3.428	0.549	0.291	0.422
CAUTIOUS	0.146	0.356	0.005	0.010
HUNKERED DOWN	0.999	0.005	0.114	0.362

XSTAT= 6.6876

P-VALUE = 0.3507

CRITICAL VALUE = 12.5916

ALPHA = 0.05

---------------------------------------------------------------------------------------------------------------------

The question that needs to be answered is:

What is the final conclusion of this problem?

Select one:

A. The two categorical: Consumer segment and Geographic region are dependent

B. The two categorical: Consumer segment and Geographic region have some relationship

C. The average feedback for each regions are different

D. The two categorical: Consumer segment and Geographic region are independent

Answer 1

Given that

Test statistics =

Critical value :

P-VALUE = 0.3507

Claim : To test whether that the Consumer segment and Geographic region are dependent or not

Hypothesis : Ho :  Consumer segment and Geographic region are independent

H1 :  Consumer segment and Geographic region are dependent

Decision Rule :   We Fail to Reject Ho

Conclusion : There is sufficient evidence to conclude that Consumer segment and Geographic region are independent

Option D is correct