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 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 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

Required:
a. Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company. What is the p-value and what is your conculsion??
b. If there is a dependence or association between the two ratings, discuss and use the probabilities to justify your answer.

Answer 1

p value = 0.001908

There is no dependence

Explanation:

We have

H0 : quality of management and reputation are independent

H1: they are not independent

We have df to be

(3-1)(3-1) = 4

We get the test statistic

Chi-square = 17.028

Using the Chi-square table

P value = 0.001908

Since p value is less than 0.05

We reject the null hypothesis. There is evidence that the quality of management and also reputation of company are not independent

B.

This p value tells us there is no dependence. The probability that they would show dependence has been given by the p value as 0.001908