Green Valley

Topics: Standard deviation, Statistical hypothesis testing, Arithmetic mean Pages: 5 (934 words) Published: February 6, 2012

CASE STUDY Green Valley


Green Valley Assembly Company is an establishment that assembles electronic products for manufacturers that require temporary extra production capacity. Green Valley Assembly frequently works under the label of popular manufacturers where high quality is a basic requirement. Recently, Tom Bradley and Sandra Hansen of the Green Valley personnel department have shown interest in implementing a job-enrichment program into the assembly operation. They decided to introduce the program in one wing of the plant and continue with the current method the other wing and after six months, compare the results.

After the six month trial period, Tom and Sandra collected data from the two random samples. Each sample (represented by n1 and n2) produced sample means (represented by x1 and x2) and sample standard deviations (represented by s1 and s2) and this would determine whether the consistency of the employees has been affected by the new program. However, there is also concern on whether the job-enrichment program has caused a change in the number of defective products. So they produced another test to determine the whether the job-enrichment program affected the quality of the products.
The analysis includes two tests. The first test conducted was a hypothesis test to determine whether the job-enrichment program changed the average output. The second test performed measured whether the job-enrichment program reduced the proportion of defective products. PHStat was used to calculate t-scores, z-scores and critical values needed in order to determine whether the program would be rejected.

Results from the first hypothesis test determined that the job-enrichment program did not consistently turn out a better average output rate. Results from the second hypothesis test determined that the job-enrichment program did not reliably reduce the rate of defective products. Therefore, it is recommended that Green Valley Assembly Company should not implement the new job-enrichment program since training can be very costly and would not effectively improve production rates.


This first test determines whether the job-enrichment program has changed the average output produced by their workers.

1. Determine the null and alternative hypothesis.
H0: μ1 ≤ μ2or μ1-μ2 ≤ 0.0
HA;μ1 > μ2orμ1-μ2 < 0.0
(where μ1 = old and μ2 = job enriched)

2. Test while using a level of significance of α = 0.05
3. Compute the test statistic since population standard deviations are unknown.

Old Method|  |
Sample Size (n1)| 50|
Sample Mean(X1)| 11|
Sample Standard Deviation (s1)| 1.2|
Job Enriched|  |
Sample Size(n2)| 50|
Sample Mean(X2)| 9.7|
Sample Standard Deviation (s2)| 0.9|

t Test Statistic| 6.128259|

4. Determine the decision rule.

Upper-Tail Test|  |
Upper Critical Value| 1.660551|
p-Value| 9.3E-09|

If t < -1.6605, reject the null hypothesis.
If t > -1.6605, do not reject the null hypothesis.

t = 6.1263 > 1.6605

Based upon this data, we should reject not the null hypothesis. This means that we do not have enough evidence to determine whether or not the mean of the average of output made by the job-enrichment surpasses the mean average of the old wing and its consistency.

The second test determines whether the samples are producing a different average output rate of defective products.

1. Determine the null and alternative hypothesis.
H0: π1 ≤ π2or π1-π2 ≤ 0
HA;π1 > π2orπ1-π2 > 0
(where π1 = old and π2= job-enriched)

2. Test while using a level of significance of α = 0.05
3. Compute the z statistic for the difference...
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