Question

2. Using the worksheet, Quality, determine which wing of the company produces higher quality parts: Old Wing

and Job-enriched Wing. Assume Alpha 0.01 round to four decimals.

a. Which statistical analysis should be used to answer this question?

b. What are the null and alternative hypotheses?

c. Conduct the appropriate statistical analysis on Excel or StatCrunch. Provide a copy of your output.

d. Using your output, what is the p-value?

e. Using your output, what is the test statistic?

f. What is your decision?

g. Based on your decision, what is your conclusion?

3. Based on the analyses conducted in Questions #1 and #2, what conclusion do you reach about the success of the

Job Enrichment program? Support your answer with your analyses and decisions.

Quality Sheet below:

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

From the given data, we calculate the frequency of Defective and Non-Defective for both Wings

	Old Wing	Job-Enriched Wing
Defective	10	11
Not Defective	69	112
Total	79	123

Group 1 (Old Wing)

Proportion of Defective Parts (p₁) = 10/79 = 0.127

n₁ = 79

Group 2 (Job-Enriched Wing)

Proportion of Defective Parts (p₂) = 11/123 = 0.089

n₂ = 123

p_c = (n₁*p₁ + n₂*p₂)/(n₁+n₂) = 0.104

Standard Error (SE) = (p_c*(1-p_c)/n₁ + p_c*(1-p_c)/n₂ )^1/2 = 0.044

Alpha = 0.05

a)

We will be using one tailed z test of diff of population proportions

b)

Null and Alternate Hypothesis

H₀: p₁ = p₂ (The Proportion of defective parts is same for both wings)

H_a: p₁ > p₂ (The Proportion of defective parts for Old 1 is greater than that of Job-Enriched Wing)

c)

I have used excel but there is no tool to do the hypothesis test. Instead I have calculated values as shown above

d)

Test Statistic

Z = (p₁-p₂)/SE = 0.844

p-value = 1- NORM.S.DIST(0.844,TRUE) = 0.1993

e)

Test Statistic

Z = (p₁-p₂)/SE = 0.844

f)

Result

Since the p-value is greater than 0.05, the data is not statistically significant and we fail to reject the null hypothesis.

g)

The Proportion of defective parts is same for both wings

Question 3 cannot be answered without 1.