Question

You may need to use the appropriate technology to answer this question. 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

Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company.

a. State the null and alternative hypotheses.
b. Find the value of the test statistic. (Round your answer to three decimal places.)
c. Find the p-value. (Round your answer to four decimal places.)

Answer 1

Explanation:

The null and alternative hypothesis:

`H_o \text{: Quality of management and reputation of company are independent}`

`H_a \text{: Quality of management is not independent of the reputation of company }`

The observed values:

Excellent Good Fair Total

Excellent 40 25 8 73

Good 35 35 10 80

Fair 25 10 12 47

Total 100 70 30 200

The expected values = (Row total/column total)/grand total)

Excellent Good Fair

Excellent 36.5 25.55 10.95

Good 40 28 12

Fair 23.5 16.45 7.05

O E (O - E)²/E

40 36.5 0.3356

35 40 0.6250

25 23.5 0.0957

25 25.55 0.0118

35 28 1.7500

10 16.45 2.5290

8 10.95 0.7947

10 12 0.3333

12 7.05 3.4755

9.951

`X^2 = \sum ((O-E)^2)/(E) \\ \\ \mathbf{X^2 = 9.951}`

Degree of freedom
`df = (r-1)(c-1)`

`df = (3 - 1 ) (3 - 1)`

`df = (2)(2)`

`df = 4`

Using Excel formula =CHIDIST(x²,d.f)

The P-value = 0.0413