Wall Street Joumal Corporate Percuptions Sudy 2011 surveyed readers and asked ho
ID: 3275858 • Letter: W
Question
Wall Street Joumal Corporate Percuptions Sudy 2011 surveyed readers and asked how each rated 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. Reputation of Company Good 25 35 10 Fair Quality of Management Excellent Good Fair Excellent 40 35 25 10 15 Use a.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 conclusion? If there is a dependence or association between the two ratings, discuss and use prob- abilities to justify your answer. a. b.Explanation / Answer
H0: The quality of management and the reputation of the company are independent.
H1: The quality of management and the reputation of the company are not independent.
The test statistic is
chi-square = sum (O-E)^2/E =
= 0.71429 + 0.0102 +2.8809+0.625+1.75 +0.3333 +0+3.2143+7.5
= 17.02806
The critical chi-square for df = (r-1)(c-1) = (3-1)(3-1)= 4 and alpha = 0.05 is chi-square = 9.4877.
The test statistic of 17.02806 > 9.4877, so we reject the null hypothesis H0.
The p-value = 0.001909.
Interpretation:
The quality of management and the reputation of the company are not independent.
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