Question

The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the Quality of Management and the Reputation of the Company for over 250 world-wide corporations. Both the Quality of Management and the Reputation of the Company were rated on an Excellent, Good, and Fair categorical scale. Assume the sample data for 200 respondents below applies to this study.

	Reputation of Company
Quality of Management	Excellent	Good	Fair
Excellent	40	25	5
Good	35	35	10
Fair	25	10	15

a. Use a .05 level of significance and test for independence of the quality of management and the reputation of the company. Use Table 12.4.

Compute the value of the  ² test statistic (to 2 decimals).

The p-value is - Select your answer -less than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2

What is your conclusion?
- Select your answer -Conclude that the rating for the quality of management is not independent of the rating for the reputation of the company.Conclude that the rating for the quality of management is independent of the rating for the reputation of the company.Item 3

b. If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.
- Select your answer -The highest probabilities are that the two variables will have the same ratings and associated.The highest probabilities are that the two variables will have the same ratings but not associated.The highest probabilities are that the two variables will not have the same ratings but not associated.Item 4

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	excellent	good	fair	Total
	E	35.000	24.500	10.500	70.00
	G	40.000	28.000	12.000	80.00
	F	25.000	17.500	7.500	50.00
	total	100.00	70.00	30.00	200.00
chi square    χ2	=(Oi-Ei)2/Ei	excellent	good	fair	Total
	E	0.714	0.010	2.881	3.6054
	G	0.625	1.7500	0.3333	2.7083
	F	0.000	3.2143	7.5000	10.7143
	total	1.3393	4.9745	10.7143	17.028
test statistic X2 =		17.03

p value is less than .005

Conclude that the rating for the quality of management is not independent of the rating for the reputation of the company.

b)

-The highest probabilities are that the two variables will have the same ratings and associated