Question

Two factories located in different cities, owned by the same organization (ABC Corp), produce the identical product. The product they make is a specialized all-terrain vehicle. In 2002, based on productivity data from a random sample of workers, management felt the average labor productivity of the two plants could be improved. So, both plants underwent identical process improvements through 2003. In 2004, the worker productivity was gauged for both plants using the same set of workers.

Factory A Before	Factory A After	Factory B Before	Factory B After
6	8	3	6
5	5	8	6
6	8	3	5
7	6	7	7
9	9	6	9
5	6	4	4
4	5	8	9
6	5	4	5
5	6	6	5
7	8	2	4
8	7	8	7
4	5	5	9
5	8	3	3
4	5	9	6
9	7	6	8
8	8	3	6
3	6	7	5
7	5	4	8
4	7	7	5
2	4	5	7

Factory A Before = worker productivity for Factory A measured in units finished per day measured in 2002 i.e. before improvement intervention

Factory B Before = worker productivity for Factory B measured in units finished per day measured in 2002 i.e. before improvement intervention

Factory A After = worker productivity for Factory A measured in units finished per day measured in 2004 i.e. after improvement intervention

Factory B After = worker productivity for Factory B measured in units finished per day measured in 2004 i.e. after improvement intervention

You are the consultant and the management wants the following questions answered.

1. Was there a difference in average worker productivity between factories A and B before the process improvement began?
2. Do the two factories (A and B) differ in terms of average productivity after the process improvement?
3. Did the process improvement intervention help improve the average worker productivity in ABC Corp?
4. Did the process improvement intervention help improve the average worker productivity in factory A?
5. Did the process improvement intervention help improve the average worker productivity in factory B?
6. Did the average worker productivity in Factory A improve more than the average worker productivity in Factory B?

Assume α-level of 10%. You have to use p value method. Assume equal variances wherever needed.

Answer 1

a.

t-Test: Two-Sample Assuming Equal Variances
	Factory A before	Factory B before
Mean	5.684210526	5.526315789
Variance	4.005847953	4.263157895
Observations	19	19
Pooled Variance	4.134502924
Hypothesized Mean Difference	0
df	36
t Stat	0.239341388
P(T<=t) one-tail	0.40609916
t Critical one-tail	1.305513886
P(T<=t) two-tail	0.81219832
t Critical two-tail	1.688297714

Since p-value=0.8122>0.1 so there is insufficient evidence to conclude that there is a difference in average worker productivity between factories A and B before the process improvement began.

b.

t-Test: Two-Sample Assuming Equal Variances
	Factory A After	Factory B After
Mean	6.315789474	6.210526316
Variance	2.005847953	3.286549708
Observations	19	19
Pooled Variance	2.64619883
Hypothesized Mean Difference	0
df	36
t Stat	0.199446749
P(T<=t) one-tail	0.421517789
t Critical one-tail	1.305513886
P(T<=t) two-tail	0.843035579
t Critical two-tail	1.688297714

Since p-value=0.8430>0.1 so there is insufficient evidence to conclude that the two factories (A and B) differ in terms of average productivity after the process improvement.

c.

t-Test: Two-Sample Assuming Equal Variances
	Before	After
Mean	5.538461538	6.256410256
Variance	4.097165992	2.511470985
Observations	39	39
Pooled Variance	3.304318489
Hypothesized Mean Difference	0
df	76
t Stat	-1.744093565
P(T<=t) one-tail	0.042592979
t Critical one-tail	1.292790268
P(T<=t) two-tail	0.085185957
t Critical two-tail	1.665151353

Since p-value=0.0426<0.1 so there is sufficient evidence to conclude that  the process improvement intervention helps to improve the average worker productivity in ABC Corp.

d.

t-Test: Two-Sample Assuming Equal Variances (Factory A)
	Before	After
Mean	5.684210526	6.315789474
Variance	4.005847953	2.005847953
Observations	19	19
Pooled Variance	3.005847953
Hypothesized Mean Difference	0
df	36
t Stat	-1.122809151
P(T<=t) one-tail	0.134475592
t Critical one-tail	1.305513886
P(T<=t) two-tail	0.268951185
t Critical two-tail	1.688297714

Since p-value=0.1345>0.1 so there is insufficient evidence to conclude that  the process improvement intervention helps to improve the average worker productivity in factory A.

e.

t-Test: Two-Sample Assuming Equal Variances
	Before	After
Mean	5.526315789	6.210526316
Variance	4.263157895	3.286549708
Observations	19	19
Pooled Variance	3.774853801
Hypothesized Mean Difference	0
df	36
t Stat	-1.085429163
P(T<=t) one-tail	0.142473435
t Critical one-tail	1.305513886
P(T<=t) two-tail	0.284946871
t Critical two-tail	1.688297714

Since p-value=0.1425>0.1 so there is insufficient evidence to conclude that  the process improvement intervention helps to improve the average worker productivity in factory B.

f.

t-Test: Two-Sample Assuming Equal Variances
	Factory A	Factory B
Mean	6.051282051	5.871794872
Variance	3.049932524	3.69365722
Observations	39	39
Pooled Variance	3.371794872
Hypothesized Mean Difference	0
df	76
t Stat	0.431638491
P(T<=t) one-tail	0.333613107
t Critical one-tail	1.292790268
P(T<=t) two-tail	0.667226213
t Critical two-tail	1.665151353

p-value=0.3336>0.1 so there is insufficient evidence to conclude that the average worker productivity in Factory A improves more than the average worker productivity in Factory B.