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 worldwide corporations. Quality of management is rated on a scale of exceptional, moderate, and needs improvement categorical scale. And company reputation is rated on a scale of excellent, good, and fair categorical scale. Assume the sample data for the respondents are below:

	Excellent	Good	Fair
Exceptional	40	25	5
Moderate	35	38	10
Needs Improvement	25	10	15

To conduct a Chi-Square testing to analyze the independence of two variables, we must construct an expected frequency table. Provide the value that would go into the box with the ???

	Excellent	Good	Fair
Exceptional
Moderate
Needs Improvement		??

Note: as always, enter your response in 4 decimal places.

Answer 1

	Excellent	Good	Fair	Total
Exceptional	40	25	5	70
Moderate	35	38	10	83
Needs improvement	25	10	15	50
Total	100	73	30	203

Now we will make the expected frequency table;

	Excellent	Good	Fair
Exceptional	(exceptional total * excellent total)/(grand total) = (70 * 100) / (203) = 34.4828	(Exceptional total * good total) / (grand total) = (70 * 73) / (203) = 25.1724	(70*30)/(203)=10.3448
Moderate	(moderate total * excellent total) / (grand total) = (83 * 100) / (203) = 40.8867	(83 * 73) / (203) = 29.8473	(83 * 30) / (203) = 12.2660
Needs improvement	(need improvement total * excellent total) / (grand total) = (50 * 100) / (203) = 24.6305	(50 * 73 ) / (203) = 17.9803	(50 * 30) * (203) = 7.3892

Expected value = for every cell multiply each row total by each column total and divide it by over all total.