The Wall Street Journal Corporate Perceptions Study surveys readers and asks how each rats the quality of management and the reputation of the company for over 250 worldwide 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. Excel File: data12-13.xlsx Reputation of Company Quality of Management Excellent Good Fair Excellent 40 25 Good 35 35 10 Fair 25 10 15 a. Use a = 0.05 level of significance and test for independence of the quality of management and the reputation of the company. Compute the value of the x test statistic (to 2 decimals). Do not round intermediate calculations. Use Table 3 of Appendix B to find the p-value. The p-value is - Select your answer - What is your conclusion? Conclude that the rating for the quality of management is Select your answer - vof the rating for the reputation of the company. b. If 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 - Select your answer -

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The Wall Street Journal Corporate Perceptions Study surveys readers and asks how each rates the quality of management and the reputation of the company for over 250 worldwide 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.

### Data Summary

**Excel File:** [data12-13.xlsx]

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

### Analysis Tasks

**a.** Use \(\alpha = 0.05\) level of significance and test for independence of the quality of management and the reputation of the company.

- Compute the value of the \(\chi^2\) test statistic (to 2 decimals). Do not round intermediate calculations.
- Use Table 3 of Appendix B to find the \(p\)-value.
- Indicate your conclusion by selecting whether the rating for the quality of management is independent or dependent on the rating for the reputation of the company.

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

- Explain which ratings combination is most probable based on the data (e.g., both excellent, both good, etc.).

### Instructions

1. Download the data file for detailed analysis.
2. Calculate the \(\chi^2\) statistic.
3. Determine the \(p\)-value using Table 3 of Appendix B.
4. Select appropriate conclusions for parts a and b.
Transcribed Image Text:The Wall Street Journal Corporate Perceptions Study surveys readers and asks how each rates the quality of management and the reputation of the company for over 250 worldwide 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. ### Data Summary **Excel File:** [data12-13.xlsx] | Quality of Management / Reputation of Company | Excellent | Good | Fair | |-----------------------------------------------|-----------|------|------| | Excellent | 40 | 25 | 5 | | Good | 35 | 35 | 10 | | Fair | 25 | 10 | 15 | ### Analysis Tasks **a.** Use \(\alpha = 0.05\) level of significance and test for independence of the quality of management and the reputation of the company. - Compute the value of the \(\chi^2\) test statistic (to 2 decimals). Do not round intermediate calculations. - Use Table 3 of Appendix B to find the \(p\)-value. - Indicate your conclusion by selecting whether the rating for the quality of management is independent or dependent on the rating for the reputation of the company. **b.** If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer. - Explain which ratings combination is most probable based on the data (e.g., both excellent, both good, etc.). ### Instructions 1. Download the data file for detailed analysis. 2. Calculate the \(\chi^2\) statistic. 3. Determine the \(p\)-value using Table 3 of Appendix B. 4. Select appropriate conclusions for parts a and b.
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