Question

Levi-Strauss Co manufactures clothing. The quality control department measures weekly values of different suppliers for the percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up). The data is in the following table, and there are some negative values because sometimes the supplier is able to layout the pattern better than the computer ("Waste run up," 2013).

Table #11.3.3: Run-ups for Different Plants Making Levi Strauss Clothing

Plant 1	Plant 2	Plant 3	Plant 4	Plant 5
1.2	16.4	12.1	11.5	24
10.1	-6	9.7	10.2	-3.7
-2	-11.6	7.4	3.8	8.2
1.5	-1.3	-2.1	8.3	9.2
-3	4	10.1	6.6	-9.3
-0.7	17	4.7	10.2	8
3.2	3.8	4.6	8.8	15.8
2.7	4.3	3.9	2.7	22.3
-3.2	10.4	3.6	5.1	3.1
-1.7	4.2	9.6	11.2	16.8
2.4	8.5	9.8	5.9	11.3
0.3	6.3	6.5	13	12.3
3.5	9	5.7	6.8	16.9
-0.8	7.1	5.1	14.5
19.4	4.3	3.4	5.2
2.8	19.7	-0.8	7.3
13	3	-3.9	7.1
42.7	7.6	0.9	3.4
1.4	70.2	1.5	0.7
3	8.5
2.4	6
1.3	2.9

Do the data show that there is a difference between some of the suppliers? Test at the 1% level

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Let x₁ = percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up) from plant 1

Let x₂ = percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 2

Let x₃ = percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 3

Let x₄ = percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 4

Let x₅ = percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 5

Let ?₁ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 1

Let ?₂ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 2

Let ?₃ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 3

Let ?₄ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 4

Let ?₅ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 5

(i) Which of the following statements correctly defines the null hypothesis H_O?

A. All five mean percentage differences are equal

B. Two of the mean percentage differences are not equal

C. At least four of the mean percentage differences are equal

D. At least two of the mean percentage differences are not equal

Enter letter corresponding to correct answer

Let ?₁ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 1

Let ?₂ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 2

Let ?₃ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 3

Let ?₄ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 4

Let ?₅ = mean percentage difference of waste between the layout on the computer and the actual waste of run-up from plant 5

(ii) Which of the following statements correctly defines the alternate hypothesis H_A?

A. All five mean percentage differences are equal

B. Two of the mean percentage differences are not equal

C. At least four of the mean percentage differences are equal

D. At least two of the mean percentage differences are not equal

Enter letter corresponding to correct answer

(iii) Enter the level of significance ? used for this test:

Enter in decimal form. Examples of correctly entered answers: 0.01    0.02    0.05    0.10

(iii) Calculate sample mean and sample standard deviation for Plant 1 sample

Enter sample mean in decimal form to nearest hundredth, then comma, then sample standard deviation in decimal form to nearest hundredth. Examples of correctly entered answers:

13.27,2.31

0.27,0.06

-10.30,0.79

(v) Calculate sample mean and sample standard deviation for Plant 2 sample

Enter sample mean in decimal form to nearest hundredth, then comma, then sample standard deviation in decimal form to nearest hundredth. Examples of correctly entered answers:

13.27,2.31

0.27,0.06

-10.30,0.79

(vi) Calculate sample mean and sample standard deviation for Plant 3 sample

Enter sample mean in decimal form to nearest hundredth, then comma, then sample standard deviation in decimal form to nearest hundredth. Examples of correctly entered answers:

13.27,2.31

0.27,0.06

-10.30,0.79

(vii) Calculate sample mean and sample standard deviation for Plant 4 sample

Enter sample mean in decimal form to nearest hundredth, then comma, then sample standard deviation in decimal form to nearest hundredth. Examples of correctly entered answers:

13.27,2.31

0.27,0.06

-10.30,0.79

(viii) Calculate sample mean and sample standard deviation for Plant 5 sample

Enter sample mean in decimal form to nearest hundredth, then comma, then sample standard deviation in decimal form to nearest hundredth. Examples of correctly entered answers:

13.27,2.31

0.27,0.06

-10.30,0.79

(ix) Using technology, determine F ratio test statistic and corresponding p-value.

Use "CTRL-click" to access link. Enter test statistic to nearest hundredth, then enter comma, then enter p-value to nearest thousandth. Examples of correctly entered responses:

12.33,0.004   

7.50,0.000

6.77,0.504

(x) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

Enter letter corresponding to correct answer.

(xi) Select the statement that most correctly interprets the result of this test:

A. The result is not statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that there is a difference between some of the suppliers.

B. The result is statistically significant at .01 level of significance. There is not enough evidence to support the claim that there is a difference between some of the suppliers.

C. The result is statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that there is a difference between some of the suppliers.

D. The result is not statistically significant at .01 level of significance. There is not enough evidence to support the claim that there is a difference between some of the suppliers.

Answer 1

Solution: (i) Which of the following statements correctly defines the null hypothesis HO?

Answer:? A. All five mean percentage differences are equal

(ii) Which of the following statements correctly defines the alternate hypothesis HA?

Answer: D. At least two of the mean percentage differences are not equal

(iii) Enter the level of significance ? used for this test:

Answer:

(iv) Calculate sample mean and sample standard deviation for Plant 1 sample

Answer:

(v) Calculate sample mean and sample standard deviation for Plant 2 sample

Answer:

(vi) Calculate sample mean and sample standard deviation for Plant 3 sample

Answer:

(vii) Calculate sample mean and sample standard deviation for Plant 4 sample

Answer:

(viii) Calculate sample mean and sample standard deviation for Plant 5 sample

Answer:

(ix) Using technology, determine F ratio test statistic and corresponding p-value.

Answer:

(x) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?

Answer: Fail to reject Ho

(xi) Select the statement that most correctly interprets the result of this test:

Answer: D. The result is not statistically significant at .01 level of significance. There is not enough evidence to support the claim that there is a difference between some of the suppliers.