Question

The Walf 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 Good Fair 40 35 25 25 35 10 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 X test statistic (to 2 decimals). The p-value is between 01 and.025 What is your conclusion? Conclude that the rating for the quality of management is not independent of the rating for the reputation of the company, Y b. Il there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer The highest probabilities are that the two variables will have the same ratings but not associated

Answer 1

Using formula E = (R*C)/n, we compute expected value for each cell. Then we find chi square value. Its value comes out to be 17.03. Next

r = 3, c = 3. Therefore r-1 = 2, c-1 = 2. Hence df = (r-1) * (c-1) = 2 * 2 = 4

Using table, we find p value which is

p- value = 0.0019

Now alpha = 0.05

As p value is less than alpha, so we reject Ho. We conclude that rating for the quality of management is not independent of the rating of the reputation of company.

There is association between two ratings. The highest probabilities are that the two variables have same rating.