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. 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.
Quality of Management | Reputation of Company | ||
---|---|---|---|
Excellent | Good | Fair | |
Excellent | 40 | 25 | 5 |
Good | 35 | 28 | 10 |
Fair | 25 | 17 | 15 |
(a)
Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company.
State the null and alternative hypotheses.
H0: Quality of management is independent of
the reputation of the company.
Ha: The proportion of companies with excellent
management is equal across companies with differing
reputations.H0: Quality of management is not
independent of the reputation of the company.
Ha: The proportion of companies with excellent
management is not equal across companies with differing
reputations. H0: Quality
of management is not independent of the reputation of the
company.
Ha: Quality of management is independent of the
reputation of the company.H0: Quality of
management is independent of the reputation of the company.
Ha: Quality of management is not independent of
the reputation of the company.
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Do not reject H0. We cannot conclude that the rating for the quality of management is independent of the rating of the reputation of the company.Do not reject H0. We cannot conclude that the ratings for the quality of management and the reputation of the company are not independent. Reject H0. We conclude that the rating for the quality of management is not independent of the rating for the reputation of the company.Reject H0. We conclude that the rating for the quality of management is independent of 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.
For companies with an excellent reputation, the largest column probability corresponds to ---Select--- excellent good fair management quality. For companies with a good reputation, the largest column probability corresponds to ---Select--- excellent good fair management quality. For companies with a fair reputation, the largest column probability corresponds to ---Select--- excellent good fair management quality. Since these highest probabilities correspond to ---Select--- the same different ratings of quality of management and reputation, the two ratings are ---Select--- independent associated .
H0: Quality of management is independent of
the reputation of the company.
Ha: Quality of management is not independent of
the reputation of the company.
Applying chi square test of independence: |
Expected | Ei=row total*column total/grand total | excellent | good | fair | Total |
excellent | 35.00 | 24.50 | 10.50 | 70 | |
good | 36.50 | 25.55 | 10.95 | 73 | |
Fair | 28.50 | 19.95 | 8.55 | 57 | |
total | 100 | 70 | 30 | 200 | |
chi square χ2 | =(Oi-Ei)2/Ei | excellent | good | fair | Total |
excellent | 0.7143 | 0.0102 | 2.8810 | 3.6054 | |
good | 0.0616 | 0.2349 | 0.0824 | 0.3790 | |
Fair | 0.4298 | 0.4362 | 4.8658 | 5.7318 | |
total | 1.2058 | 0.6814 | 7.8292 | 9.7163 |
test statistic X2 = | 9.716 | |
p value = | 0.0455 |
as p value is less than 0.05 level
Reject H0. We conclude that the rating for the quality of management is not independent of the rating for the reputation of the company
b)
For companies with an excellent reputation, the largest column probability corresponds to -excellent management quality. For companies with a good reputation, the largest column probability corresponds to good management quality. For companies with a fair reputation, the largest column probability corresponds to fair management quality. Since these highest probabilities correspond to -- the same ratings of quality of management and reputation, the two ratings are associated .
The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the...
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. 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. Quality of Management Reputation of Company Excellent Good Fair Excellent 40 25 5 Good 35 28 10...
The Wal 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, 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 respendents below applies to this study Reputation of Company Quality of Management Good Fair Excellent Excellent 40 25 5 Good 35 28 10...
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