Question

Most global organizations consider aligning an incentives and rewards system with employee roles critical to success. However, is there a difference among North American, European, and Asian organizations in the proportion of organizations that are adopting an incentives and rewards system that aligns with employee roles? A random sample of 183 North American organizations, 160 European organizations, and 138 Asian organizations were surveyed and were asked to indicate if they are adopting an incentives and rewards system that aligns with employee roles. The study showed that 135 North American organizations, 98 European organizations, and 78 Asian organizations are adopting an incentives and rewards system that aligns with employee roles.

a. What are the null and alternate hypothesis for determining if there is a difference among the global regions in the proportion of firms that are adopting an incentives and rewards system that aligns with employee roles? State the test that should be conducted and reason.

H0:

H1:

Test to be used and reason:

b. To test your claims, you need to construct a contingency frequency table for the two categorical variables with their categories. You decide to start with the following data. Fill in the blank in the data table and contingency frequency table below:

Data

Level of Significance

0.01

Number of Rows (Variable 1)

Number of Columns (Variable 2)

Degrees of Freedom

Construct the Observed Frequency Table in the following space. Fill in the variable names at the top of the rows and columns.

Observed Frequencies

c. Construct the Expected Frequencies table in the space below. Fill in the variable names at the top of the rows and columns.

Expected Frequencies

d. Find the test statistic. Use the space below for the calculation.

Test Statistic

e. Find the critical value at the 0.01 level of significance.

Critical Value

f. At the 0.01 level of significance, is there evidence of a difference among the global regions with respect to the proportion of firms that are adopting an incentives and rewards system that aligns with employee roles? Explain how you made the decision.

Answer 1

(a)

H0: Null Hypothesis: There is no difference among the global regions in the proportion of firms that are adopting an incentives and rewards system that aligns with employee roles

HA:Alternative Hypothesis: There is a difference among the global regions in the proportion of firms that are adopting an incentives and rewards system that aligns with employee roles (Claim)

Test to be used and reason: Chi Square Test of Independence because Both the variables: (i) Global regions and (ii) adopting an incentives and rewards system that aligns with employee roles or not. The researcher question is: Is there a difference among the global regions in the proportion of firms that are adopting an incentives and rewards system that aligns with employee roles?

(b)

(i) Level of Significance : 0.01

(ii) Number of Rows (Variable 1) : 2

(iii) Number of Columns (Variable 2) : 3

(iv) Degrees of Freedom : (r - 1) X (c - 1) = (2 - 1) X(3 - 1) = 2

(v)

Observed Frequencies:

	North American organizations	European organizations	Asian organizations	Total
adopting an incentives and rewards system that aligns with employee roles.	135	98	78	311
Not adopting an incentives and rewards system that aligns with employee roles.	48	62	60	170
Total	183	160	138	481

(c)

Expected Frequencies:

	North American organizations	European organizations	Asian organizations	Total
adopting an incentives and rewards system that aligns with employee roles.	183X311/481=118.322	160X311/481=103.451	138X311/481=89.221	311
Not adopting an incentives and rewards system that aligns with employee roles.	183X170/481=64.678	160X170/481=56.549	138X170/481=48.773	170
Total	183	160	138	481

(d)

Test Statistic () is calculated as follows:

Observed (O)	Expected (E)	(O - E)2/E
135	118.322	2.351
98	103.451	0.287
78	89.227	1.413
48	64.678	4.301
62	56.549	0.525
60	48.773	2.584
Total = Test Statistic () =		11.461

(e)

From Table,

critical value of = 9.21

(f)

At the 0.01 level of significance, there is evidence of a difference among the global regions with respect to the proportion of firms that are adopting an incentives and rewards system that aligns with employee roles.

Explanation:
Since calculated value of = 11.461 is greater than critical value of = 9.21, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that there is a difference among the global regions in the proportion of firms that are adopting an incentives and rewards system that aligns with employee roles.