Corporate Perceptions Study 2011 surveyed readers and asked how each rate- 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. The Wall Streer Jou quality of management and the Reputation of Company Quality of Management 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. O H,1 Quality of management is not independent of the reputation of the company. H, The proportion of companies with excellent management is not equal across companies with differing reputations. • H,1 Quality of management is independent of the reputation of the company. H Quality of management is not independent of the reputation of the company. O H,: Quality of management is independent of the reputation of the company. H The proportion of companies with excellent management is equal across companies with differing reputations. O H,: Quality of management is not independent of the reputation of the company. H,: Quality of management is 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. O Do not reject H, We cannot conclude that the rating for the quality of management is independent of the rating of the reputation of the company. O Reject H,. We conclude that the rating for the quality of management is independent of the rating for the reputation of the company. O Reject H,. We conclude that the rating for the quality of management is not independent of the rating for the reputation of th сompany, O Do not reject H, We cannot conclude that the ratings for the quality of management and the reputation of the company are not independent. (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--- V management quality. For companies with a good reputation, the largest column probability corresponds to -Select-V management quality. For companies with a fair reputation, the largest column probability corresponds to -Select- v management quality. Since these highest probabilities correspond to -Select-- v ratings of quality of management and reputation, the two ratings are -Select--