Question

Problem 3: A Corporate Perceptions Study surveyed 200 readers and asked them on how they would rate XYZ Corporation on the “Quality of Management” and the “Reputation of the Company”. The two variables of the study were rated on a categorical scale as excellent, good, and fair. The sample data on 200 responses for the study is summarized as follows. Conduct an appropriate hypothesis test for this problem to check if the variables are independent of each other. Reputation of Company Quality of Management Excellent Good Fair Excellent 39 26 5 Good 36 34 10 Fair 25 10 15 Answer the following questions based on your analysis. Problem 3a) Name the two variables examined in the study. Problem 3b) State the Null and Alternate Hypotheses for this test. Problem 3c) Calculate and show Expected Frequencies in a table.

Answer 1

a)

Independentness of Two variables are "Quality of Management" and "Reputation of the Company"

b)

H0: "Quality of Management" and "Reputation of the Company" are independent

Ha: "Quality of Management" and "Reputation of the Company" are not independent

c)

From the given data we have below observed frequencies

Observed	Quality of management
	Excellent	Good	Fair	total
Excellent	39	26	5	70
Good	36	34	10	80
Fair	25	10	15	50
Total	100	70	30	200

Calculate expected frequencies for above observed frequencies as sum(col)*sum(row)/total

Below table shows all the expected frequencies

Expected
	Excellent	Good	Fair
Excellent	35.000	24.500	10.500
Good	40.000	28.000	12.000
Fair	25.000	17.500	7.500