Question

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 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 nul and alternative hypotheses O H Quality of management is independent of the reputation of the company H The propoetion of companies with excellent management is equal across companies with dffering reputations O Ho Quality of management is not independent of the reputation of the company H: Quality of management is independent of the reputation of the company O Ho 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 He 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 Find the value of the test statistic. (Round your answer to three decimal places)

Answer 1

a ) H0: the quality of management is independent of the reputation of the company.

Ha: the quality of management is not independent of the reputation of the company.

b ) here we will use the chi-square test

using Minitab >stat>basic stat>tables

we have

Chi-Square Test for Association: Quality of management, Reputation of Company

Rows: Quality of management Columns: Reputation of Company

Excellent Good Fair All

Excellent    40 25 5 70
35.00 24.50 10.50
0.7143 0.0102 2.8810

Good 35 28 10 73
36.50 25.55 10.95
0.0616 0.2349 0.0824

Fair 25 17 15 57
28.50 19.95 8.55
0.4298 0.4362 4.8658

All 100 70 30 200

Cell Contents: Count
Expected count
Contribution to Chi-square

Pearson Chi-Square = 9.716, DF = 4, P-Value = 0.0455

the value of test statistic = 9.716

p-value = 0.0455

since p-value is less than 0.05 so we will reject Ho . we conclude that the quality of management is not independent of the reputation of the company.

b ) for this part please provide drop out values