Question

In: Statistics and Probability

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 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 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 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 not independent of the reputation of the company.
Ha: 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.

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.     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.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--- associated independent .

Solutions

Expert Solution

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.

b) applying chi square test:

Expected Ei=row total*column total/grand total excellent good fair Total
excellent 36.5000 25.5500 10.9500 73
good 40.0000 28.0000 12.0000 80
fair 23.5000 16.4500 7.0500 47
total 100 70 30 200
chi square    χ2 =(Oi-Ei)2/Ei excellent good fair Total
excellent 0.3356 0.0118 0.7947 1.1422
good 0.6250 1.7500 0.3333 2.7083
fair 0.0957 2.5290 3.4755 6.1003
total 1.0564 4.2909 4.6036 9.9508

test statistic X2 =9.951

p value =0.0413

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

For companies with an good reputation, the largest column probability corresponds to good

For companies with a fair reputation, the largest column probability corresponds to fair

the two ratings are associated


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