Question

The XYZ Corporation is interested in possible differences in days worked by salaried employees in three departments in the financial area. An analysis of 27 randomly chosen employees reveals the number of days worked data .

a) Use JMP to fit a one-way ANOVA to the data. Using alpha= 0.05 draw a conclusion for the ANOVA. Make sure you state your conclusion in the context of the problem.

b) Use tukey’s test with alpha= 0.05 to determine which departments’ workers have significantly differently number of days worked.

c) Assume that Department is a random factor, i.e., the three departments used in the analysis represent a random sample of all possible departments. Estimate the components of variance in number of days worked.

d) Determine with alpha = 0.05 if the variance in days worked is different by Department.

Employee    Department Days Worked

1 Pricing 256

2 Payables    220

3 Budgets 260

4 Pricing 233

5    Budgets    258

6    Payables 228

7 Budgets    265

8 Pricing    245

9 Pricing 244

10    Budgets 263

11    Budgets    258

12 Budgets    245

13    Payables 205

14 Payables    240

15 Pricing 242

16 Payables 239

17    Budgets    268

18    Payables    270

19 Pricing 258

20 Budgets    265

21 Pricing    233

22    Pricing    240

23 Budgets    278

24 Payables    255

25    Pricing 249

26    Payables    266

27    Payables 217

Answer 1

a.

One-way ANOVA: Department versus Days worked

Source DF SS MS F P
Days worked 2 2974 1487 6.57 0.005
Error 24 5432 226
Total 26 8406
Since p-value<0.05 so we conclude that  departments’ workers have significantly differently number of days worked.

b.

Grouping Information Using Tukey Method

Days worked N Mean Grouping
Budgets 9 262.22 A
Pricing 9 243.11 B
Payables 9 237.78 B

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Days worked

Individual confidence level = 98.02%

Days worked = Budgets subtracted from:

Days worked Lower Center Upper -+---------+---------+---------+--------
Payables -42.15 -24.44 -6.74 (--------*--------)
Pricing -36.81 -19.11 -1.41 (-------*--------)
-+---------+---------+---------+--------
-40 -20 0 20

Days worked = Payables subtracted from:

Days worked Lower Center Upper -+---------+---------+---------+--------
Pricing -12.37 5.33 23.04 (--------*--------)
-+---------+---------+---------+--------
-40 -20 0 20

We observe that C.I.s for Payables-Budgets and Payables-Pricing do not contain zero hence Payables departments’ workers have significantly differently number of days worked.

c.

d. Since from ANOVA table of part (a)  p-value<0.05,  the variance in days worked is different significantly by Department.