Question

The Purple Valley Assembly Company assembles consumer electronics products for manufacturers that need temporary extra production capacity. As such, it has periodic product changes. Because the products Purple Valley assembles are marketed under the label of well-known manufacturers, high quality is a must.

Tom Ash of the Purple Valley personnel department has been very impressed by recent research concerning job-enrichment programs. In particular, he has been impressed with the increases in quality that seem to be associated with these programs. However, some studies have shown no significant increase in quality, and they imply that the money spent on such programs has not been worthwhile.

Tom has talked to Mary Hansen, the production manager, about instituting a job-enrichment program in the assembly operation at Purple Valley. Mary was somewhat pessimistic about the potential, but she agreed to introduce the program. The plan was to implement the program in one wing of the plant and continue with the current method in the other wing. The procedure was to be in effect for six months. After that period, a test would be made to determine the effectiveness of the job-enrichment program.

After the six-month trial period, a random sample of employees from each wing produced the data that can be found in the worksheet labeled Production. This sample data shows the number of parts produced by an employee in one hour. Both Mary and Tom wonder whether the job-enrichment program has affected production output. They would like to use these sample results to determine whether the average output has changed and to determine whether the employees’ consistency has been affected by the new program.

A second random sample from each wing was selected. Quality of the products assembled was measured. Products were categorized as being Not Defective or Defective. Data can be found in the worksheet labeled Quality. Tom and Mary want to determine if the quality between the two samples is different.

With all of this data, Mary and Tom are beginning to get a little confused. However, they realize that there must be some way to use the information in order to make a judgment about the effectiveness of the job-enrichment program.

1. Using the worksheet, Quality, determine which wing of the company produces higher quality parts: Old Wing and Job-enriched Wing. Assume α = 0.01. Round to four decimal places.
   1. Which statistical analysis should be used to answer this question?
   2. What are the null and alternative hypotheses?
   3. Conduct the appropriate statistical analysis on Excel or StatCrunch. Provide a copy of your output.
   4. Using your output, what is the p-value?
   5. Using your output, what is the test statistic?
   6. What is your decision?
   7. Based on your decision, what is your conclusion?

Old Wing	Job-Enriched Wing
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Defective
Not Defective	Not Defective
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Defective
Not Defective	Not Defective
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Not Defective	Not Defective
Defective	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Not Defective
	Defective

Answer 1

a)

The two proportion z test is used to test whether the proportion of defects is different in two groups.

b)

The null and alternative hypothesis are,

c)

The z-statistic is obtained in excel using the following formula,

Where,

The screenshot is shown below,

d)

P-value

The p-value is obtained in excel using the function =NORM.S.DIST() for the obtained z statistic and two-sided alternative hypothesis.

e)

test statistic = 0.8442

f)

Since the p-value for the obtained test statistic is greater than 0.05 at a 5% significance level. The null hypothesis is not rejected.

g)

Since the null hypothesis is failed to reject, we can conclude that there is no difference in the proportion of defects between old wing and job-enriched wing.