Question

Two discussion groups are organized by randomly selected employees from each division. During the talks, the director lays out his marketing vision and employees ask questions relevant to their daily work. At the end, each employee has to rate the director on a scale from 1 to 10 (1=very bad; 10=very good). The HR department wants to know if the distribution of ratings of the marketing development employees is different among the employees of the two divisions.

a) Examine the distributions of the ratings (show histograms) by the two groups of employees and explain why a non-parametric test is justified to perform the analysis.

b) Perform an appropriate non-parametric test using a 5% significance level to determine if the distribution of ratings of the marketing development employees is different than that of the marketing operations employees. Specify any assumptions and/or conditions you need to make to apply the test and state your hypothesis clearly. Show your manual calculations.

c) Use Minitab to perform the test in b) above and compare your results

Marketing Development Employees	Marketing Operations Employees
8	9
7	8
6	7
2	8
5	10
8	9
7	6
3

Answer 1

a) By showing the histograjm

• From the histogram it is observed that the data are not obtained from normal distribution. Hence here we can't assume normal distribution. So for answering the query that whether the distribution of ratings of the marketing development employees is same or different among the employees of the two divisions, we perform non parametric test.

b.

c. Minitab output:

Mann-Whitney Test and CI: Marketing Develo, Marketing Operat

N Median
Marketing Development Employees 8 6.500
Marketing Operations Employees 7 8.000

Point estimate for ETA1-ETA2 is -2.000
95.7 Percent CI for ETA1-ETA2 is (-5.000,0.001)
W = 45.5
Test of ETA1 = ETA2 vs ETA1 not = ETA2 is significant at 0.0372
The test is significant at 0.0346 (adjusted for ties)

• Conclusion: Since p-value=0.0372<0.05 hence we reject null hypothesis and conclude that the distribution of ratings of the marketing development employees is different than that of the marketing operations employees.

Thank you !