Question

he 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 world-wide 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 respondents below applies to this study. Excel File: data12-13.xlsx a. Use level of significance and test for independence of the quality of management and the reputation of the company. Compute the value of the test statistic (to 2 decimals). Do not round intermediate calculations. The -value is - Select your answer - What is your conclusion? - Select your answer - b. If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.

Answer 1

Following are the solution to the given question:

Explanation:

`H_0:` Management quality and corporate reputation are independent.

`H_1:` Management quality and corporate reputation are not independent.

Test statistic:

`\to \chi^2 = (\sum (O-E)^2)/(E)`

`= 0.71429 + 0.0102 +2.8809+0.625+1.75 +0.3333 +0+3.2143+7.5\\\\= 17.02806`

The critical
`\chi^2` for
`df = (r-1)(c-1) = (3-1)(3-1)= 4` and
`\alpha = 0.05` is
`\chi^2= 9.4877`

Test statistic:

`17.02806 > 9.4877` therefore rejecting the null hypothesis
`H_0`.

p-value
`= 0.001909`

Interpretation:

There is no internal governance quality as well as the reputation of the organization.