The Wall Street Journal Corporate Perceptions Study 2011 sur

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.

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

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

The p-value is

What is your conclusion?

b. If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.

Solution

Doing an Expected Value Chart,          
          
35   24.5   10.5  
40   28   12  
25   17.5   7.5  
      
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    17.02806122   [ANSWER, TEST STATISTIC]  
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With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    3      
b =    3      
          
df =    4      
          
Also, the p value is          
          
P =    0.001908833   [ANSWER, P VALUE]
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Thus, as P < 0.05, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that quality of management and the reputation of the company are no independent. [conclusion]

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The P value here means that in case that there reallt is no dependence between the two ratings, the probability that they will seem to show at least this kind of strong dependence is 0.0019.