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 8 Good 35 35 10 Fair 25 10 12 (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 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. 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 independent of the reputation of the company. Ha: The proportion of companies with excellent management is equal across companies with differing reputations. 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. (A) Reject H0. We conclude that the rating for the quality of management is independent of the rating for the reputation of the company. (B) Do not reject H0. We cannot conclude that the ratings for the quality of management and the reputation of the company are not independent. (C) Reject H0. We conclude that the rating for the quality of management is not independent of the rating for the reputation of the company. (D) 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. (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 {excellent/ good/ fair} management quality. For companies with a good reputation, the largest column probability corresponds to {excellent/ good/ fair} management quality. For companies with a fair reputation, the largest column probability corresponds to { excellent/ good/ fair} management quality. Since these highest probabilities correspond to {different/ the same} ratings of quality of management and reputation, the two ratings are {independent associated} .

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 8 Good 35 35 10 Fair 25 10 12 (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 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. 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 independent of the reputation of the company. Ha: The proportion of companies with excellent management is equal across companies with differing reputations. 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. (A) Reject H0. We conclude that the rating for the quality of management is independent of the rating for the reputation of the company. (B) Do not reject H0. We cannot conclude that the ratings for the quality of management and the reputation of the company are not independent. (C) Reject H0. We conclude that the rating for the quality of management is not independent of the rating for the reputation of the company. (D) 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. (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 {excellent/ good/ fair} management quality. For companies with a good reputation, the largest column probability corresponds to {excellent/ good/ fair} management quality. For companies with a fair reputation, the largest column probability corresponds to { excellent/ good/ fair} management quality. Since these highest probabilities correspond to {different/ the same} ratings of quality of management and reputation, the two ratings are {independent associated} .

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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	8
Good	35	35	10
Fair	25	10	12

(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 not independent of the reputation of the company.
H_a: Quality of management is independent of the reputation of the company.

H₀: Quality of management is independent of the reputation of the company.
H_a: Quality of management is not independent of the reputation of the company.

H₀: Quality of management is not independent of the reputation of the company.
H_a: The proportion of companies with excellent management is not equal across companies with differing reputations.

H₀: Quality of management is independent of the reputation of the company.
H_a: The proportion of companies with excellent management is equal across companies with differing reputations.

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.

(A) Reject H₀. We conclude that the rating for the quality of management is independent of the rating for the reputation of the company.

(B) Do not reject H₀. We cannot conclude that the ratings for the quality of management and the reputation of the company are not independent.

(C) Reject H₀. We conclude that the rating for the quality of management is not independent of the rating for the reputation of the company.

(D) 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.

(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 {excellent/ good/ fair} management quality. For companies with a good reputation, the largest column probability corresponds to {excellent/ good/ fair} management quality. For companies with a fair reputation, the largest column probability corresponds to { excellent/ good/ fair} management quality. Since these highest probabilities correspond to {different/ the same} ratings of quality of management and reputation, the two ratings are {independent associated} .

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