Basilio, Renz Tyrone P.
STATS
A-232
Assignment: Module 7. ANOVA test
1. A rural bank has four branches in a certain city. The bank president was anxious that employees
were taking advantage of the bank’s substantial sick leave policy; and he alleged that it might be
associated with the branch where employees work. He requested each branch manager to submit
the records of sick leave (in days) availed of randomly select employees the previous year. The
table below shows the results. At a .01 alpha, is there significant difference on the mean number
of sick leave availed of employees from the four branches?
Branch A
Branch B
Branch C
Branch D
12
10
18
10
18
9
16
7
15
11
15
8
10
10
17
9
11
14
Total
55
51
80
34
Mean
13.75
10.2
16
8.5
Variance
12.25
0.70
2.50
1.67
Grand Mean = (13.75+10.2+16+8.5) = 12.11
4
Null Hypothesis: There is no significant difference on the mean number of sick leave availed of
employees from the four branches.
Alternative Hypothesis: There is significant difference on the mean number of sick leave
availed of employees from the four branches.
Level of significance: .01
Degree of freedom = k –1 = 4 -1 = 3
N – k = 18 – 4 = 14
Critical F value: 5.56
Normal Curve
5.56
Decision rule: Reject the null hypothesis if F > 5.56; otherwise, do not reject the null
hypothesis.
Computation:
Basilio, Renz Tyrone P.
STATS
A-232
SSA= ∑knj (xbarj – grand mean)2
= 4(13.75 – 12.11) 2 + 5(10.2-12.11)2+5(16- 12.11)2+4(8.5 – 12.11)2 = 156.79
SSW= (n1 – 1) (S21) + (n2 – 1) (S22) + (n3 – 1) (S23) + (n4 – 1) (S24)
= 3(12.25) + 4(0.70) + 4(2.50) + 3(1.67) = 54.56
SST= SSA + SSW = 156.79 + 54.56 = 211.35
MSA= SSA / k-1 = 156.79/ 4-1 = 52.26
MSW= SSW/ N- k = 54.56/ 18-4= 3.90
F = MSA/MSW = 52.26/3.90 = 13.40
Conclusion: Reject the null hypothesis, 13.40 > 5.56; which means there is significant difference
on the mean number of sick leave availed of employees from the four branches.
Recommendation: Based on the findings, it appears that certain employees at each branch are
taking advantage of their sick leave, as the mean average days of leave each branch differs
significantly. Sick leave is compensated time off from work that employees can utilize to be at
home and care for their health needs. Abusing sick days, on the other hand, not only affects
productivity but also puts additional strain on your coworkers, who will have to pick up the slack
while you are out of the office. As a result, I strongly advise the general manager to instruct each
of the branch managers to closely monitor each employee's leave and to require evidence such as
a medical certificate for the leave to be legal. This step will undoubtedly reduce the number of
sick days and, as a result, the risk of unproductiveness in the bank.
2. A student researcher studied the daily coffee consumptions (in ounces) of people from Cavite,
Laguna, Batangas, and Quezon. The table next page shows the summary results. At a .05 alpha,
is there significant difference on the mean daily coffee consumptions of the people from the four
places?
Cavite
Laguna
Batangas
Quezon
Sample
30
25
45
24
Mean
3.7
3.4
4.0
3.5
Variance
4.2
4.1
3.9
3.3
Grand Mean = (3.7 +3.4+4+3.5) / 4 = 3.65
Null Hypothesis: There is no significant difference on the mean daily coffee consumptions of
the people from the four places.
Alternative Hypothesis: There is significant difference on the mean daily coffee consumptions
of the people from the four places.
Level of Significance: .05
Degree of freedom: k-1 = 4 -1 = 3
N- k 124-4 = 120
Critical F- value: 2.68
Basilio, Renz Tyrone P.
STATS
A-232
Normal curve
2.68
Decision Rule: Reject the null hypothesis if F > 2.68; otherwise, do not reject the null
hypothesis.
Computation:
SSA= ∑knj(xbarj – grand mean)2
= 30(3.7-3.65)2+ 25(3.4-3.65)2+ 45(4.0 – 3.65)2+24(3.5-3.65)2 = 7.69
SSW= (n1 – 1) (S21) + (n2 – 1) (S22) + (n3 – 1)(S23) + (n4 – 1) (S24)
= 29(4.2) + 24(4.1) + 44(3.90) + 23(3.3) = 467.70
SST= SSA + SSW = 7.69 + 467.70 = 475.39
MSA= SSA/ k - 1 = 7.69/ 4-1 = 2.56
MSW= SSW/ N-k = 467.70/ 124 -4 = 3.90
F = MSA/MSW = 2.56/ 3.90 = 0.66
Conclusion: Do not reject the null hypothesis, 0.66 < 2.68; which means there is no significant
difference on the mean daily coffee consumptions of the people from the four places.
Recommendation: It is demonstrated that there is no significant difference in the mean daily
coffee consumptions of the people from the four areas based on the ANOVA test result, which is
less than the critical value. It's possible that this occurred since the four locations are all in the
same country and are close to one another. As a result, it is strongly advised that the researcher
increase the population of his or her study in order to conduct more diverse and realistic research.
Having said that, due to the comparable surroundings, they will be able to prevent similar
outcomes.