ANOVA

15.National Bearings manufacturers bearings at plants located in Portland Oregon, Houston Texas, and Jacksonville Florida. To measure employees knowledge of Total Quality Management(TQM), six employees were randomly selected at each plant and test. The test scores for the employees are below

Observation Portland Houston Jacksonville

1 85 71 59

2 75 75 64

3 82 73 62

4 76 74 69

5 71 69 75

6 85 82 67

Managers want to know if, on average, knowledge of TQM is equal across the 3 plants. Test equality of mean scores at =0.05

A. The F value of 9 is > the F critical value of 3.682, therefore reject the equality of means. Knowledge of TWM is not equal across the 3 plants.

B. The F value is 3.419 is < the F critical value of 3.682, therefore do not reject equality of means. Knowledge of TWM is equal across the 3 plants.

C. The F value of 1.326 is < the F critical value of 3.682, therefore do not reject equality of means. Knowledge of TWM is equal across the 3 plants.

D. The F value of 6.349 is > the F critical value of 3.682, therefore reject the equality of means. Knowledge of TQM is not equal across the 3 plants.

HINT: What statisticals procedures is used to test equality of three population means?

16.To test whether the mean time to mix a batch of adhesive is the same for machines produced by four manufacturers. TiteBondMax obtained data on the time (in minutes) needed to mix the materials, listed below

Manufacturer

A B C D

25 23 25 22

23 21 25 23

21 23 25 23

23 24 21 22

Test whether the machines have equal mean mixing time at =0.01

A. the pvalue 0.0001 is extreme evidence that the machines are not all the same.

B. the data provides insignificant evidence against H0: Equal means at pvalue 0.514. The machines are considered equal.

C. the data provides weak evidence against H0: Equal means at pvalue at pvalue 0.013. The mixing machines are not all equal.

D. the data provides weak evidence against H0: Equal means at pvalue 0.072. Equality of means remains plausible

E. None of the answers are correct

F. the data provides extreme evidence against H0: Equal means at pvalue 0.001. The mixing machines are not all equal.

HINT: We state that the evidence against H0 is:

-Extreme when p value < 0.001

-Overwhelming when 0.001 p value < 0.01

-Strong when 0.01 p value < 0.05

-Weak when 0.05 p value <0.10

-Insignificant when 0.10 p value

Pivot Table

17.To balance inventory at Otto's Optometry, customer Gender and Eye Conditions were collected in the data below

Customer # Eye Condition Gender Customer # Eye Condition Gender

1 Nearsighted Female 43 Bifocals Male

2 Bifocals Male 44 Bifocals Female

3 Nearsighted Female 45 Farsighted Male

4 Nearsighted Male 46 Nearsighted Female

5 Bifocals Female 47 Bifocals Male

6 Nearsighted Female 48 Bifocals Male

7 Nearsighted Female 49 Bifocals Female

8 Bifocals Male 50 Bifocals Female

9 Bifocals Male 51 Farsighted Male

10 Bifocals Female 52 Bifocals Female

11 Farsighted Male 53 Farsighted Male

12 Bifocals Male 54 Bifocals Male

13 Bifocals Female 55 Bifocals Female

14 Nearsighted Female 56 Bifocals Female

15 Bifocals Male 57 Nearsighted Male

16 Bifocals Female 58 Nearsighted Female

17 Bifocals Female 59 Bifocals Male

18 Farsighted Male 60 Nearsighted Male

19 Bifocals Male 61 Bifocals Male

20 Nearsighted Male 62 Farsighted Male

21 Bifocals Male 63 Bifocals Female

22 Nearsighted Female 64 Bifocals Male

23 Nearsighted Female 65 Farsighted Male

24 Bifocals Female 66 Bifocals Male

25 Bifocals Female 67 Farsighted Male

26 Farsighted Male 68 Nearsighted Female

27 Nearsighted Female 69 Bifocals Female

28 Farsighted Male 70 Farsighted Male

29 Bifocals Female 71 Nearsighted Female

30 Bifocals Female 72 Farsighted Male

31 Farsighted Male 73 Nearsighted Female

32 Farsighted Male 74 Bifocals Female

33 Bifocals Female 75 Farsighted Male

34 Nearsighted Female 76 Farsighted Female

35 Bifocals Female 77 Farsighted Female

36 Bifocals Male 78 Farsighted Female

37 Bifocals Male 79 Farsighted Female

38 Nearsighted Female 80 Farsighted Female

39 Nearsighted Male 81 Farsighted Female

40 Nearsighted Female 82 Farsighted Female

41 Bifocals Female 83 Farsighted Female

42 Bifocals Female 84 Farsighted Female

Make a 2x2 pivot table with Gender in row and Eye Condition in column. The pivot table is

A. Count of Eye Condition Column Label

Row Label Bifocals Foresighted Nearsighted Grand Total

Female 29 9 17 55

Male 9 9 11 29

Grand Total 39 18 28 84

B. Count of Eye Condition Column Label

Row Label Bifocals Foresighted Nearsighted Grand Total

Female 22 9 16 47

Male 17 15 5 37

Grand Total 39 24 21 84

C. Count of Eye Condition Column Label

Row Label Bifocals Foresighted Nearsighted Grand Total

Female 13 27 5 45

Male 8 24 7 39

Grand Total 21 51 12 84

D. Count of Gender Condition Column Label

Row Label Bifocals Foresighted Nearsighted Grand Total

Female 15 9 20 44

Male 10 15 15 40

Grand Total 25 24 35 84

E. none of the answers match my table

HINT: http://j2software.com/excelVideos/pivotTableSimple/pivotTableSimple.html

18.Given the following contingency table below with category labels A, B, C, X, Y, and Z, what is the expected count with 1 decimal place in the joint category of C and X?

X Y Z

A 18 10 15

B 15 6 2

C 14 1 5

Answer: ________

ChiSquare-Critical Value

19.What is the critical value of the significance and table parameters in the data below

Level of Significance 0.01

Number of Rows 1

Number of Columns 8

A. None of the answers are correct

B. 11.143

C. 18.475

D. 22.307

E. 5.991

HINT:DF depends on the number of rows and columns of a contingency table

ChiSquare-Test of Independence

20.Part Quality of three suppliers data are listed below

Part Quality

Supplier Good Minor Defect Major Defect

A 100 5 8

B 160 22 4

C 150 7 11

At =0.05, does Part Quality depend on Supplier, or should the cheapest Supplier be chosen?

A. Pvalue of 0.008 rejects the assumption of independence of Part Quality and Supplier. Further supplier eval is recommended

B. none of the answers fit the data

C. The assumption of independence of Part Quality and Supplier cannot be rejected. Choose the cheapest supplier.

D. Pvalue of 0.0008 rejects the assumption of independence of Part Quality and Supplier. Further supplier eval is recommended

E. Pvalue of 0.039 rejects the assumption of independence of Part Quality and Supplier. Further supplier eval is recommended

HINT:Test independence of Supplier and Part Quality

ChiSquare-Goodness of Fit

21.A sales region has been divided into five territories, each of which was believed to have equal sales potential. The actual Sales Volume for several sampled days is in the data below

Territory

A B C D E

Sales Volume 110 140 90 106 100

At =0.05, do the territories have equal Sales Volume?

A. H0: Territories have equal Sales Volume is not rejected with pvalue 0.074. The counts are consistent with the model of equal proportions.

B. none of the answers are correct

C. H0: Territories have equal Sales Volume is not rejected with pvalue 0.334. The counts are consistent with the model of equal proportions.

D. H0: Territories have equal Sales Volume is rejected with pvalue 0.012. The counts are not consistent with the model of equal proportions. Territories have unequal Sales Volume.

E. H0: Territories have equal Sales Volume is rejected with pvalue 0.041. The counts are not consistent with the model of equal proportions. Territories have unequal Sales Volume.

HINT: If the territories have equal volumes, then they should share the total volume equally. Recall the formula for DF for a tabulation of one row or one column.

Correlation-Qualitative Assessment

22.Scatter plots are used to discover relationships between variables., Using the corresponding measurements of variable1 and variable2 in the data below, ploit variable1 vs,. variable 2 and describe the correlation between variable1 and variable2

variable1 variable2

5.92418 16.01040

-2.15342 6.90096

-5.68710 3.20965

-2.35173 8.11837

9.13267 20.86393

8.84593 17.88436

0.60205 11.33976

4.30225 13.72104

-9.69073 0.22652

-6.81619 2.88607

7.00841 14.48358

4.48845 15.56499

3.06470 11.36857

-9.46731 1.14076

1.54090 12.95229

-4.20144 5.79307

6.11798 15.91570

9.94412 16.96745

1.32124 10.86254

-7.69106 1.10462

5.89874 15.93450

-0.72913 10.47150

8.39173 17.99690

-9.46846 0.72233

A. The strength of the relationship is moderate, linear, and positive

.

B. The strength of the relationship is strong, but is not linear

C. The relationship is linear, positive, and strong

D. The relationship is linear, negative, and strong

E. None of the answers accurately characterize the data

F. There is no relationship, or the strength of the relationship is very weak

G. The strength of the relationship is moderate, linear, and negative

Correlation-Quantative Evaluation

23.Correlation is used to discover relationships between variables. Evaluate the correlation between the variables using the data below

variable1 variable2

-1.60263 6.66630

5.13511 22.39796

6.36533 48.04439

5.62218 33.73949

-2.19935 13.13368

6.44037 34.07411

7.53576 57.43268

6.84911 46.18391

-0.96507 2.31758

-7.97987 66.45126

7.71148 60.12220

8.00414 69.34776

-1.84249 -8.58487

-6.64529 35.44469

3.52281 15.81326

6.12823 42.51683

-8.02429 63.53322

1.93739 10.39306

1.60250 -1.67370

9.59542 92.44574

0.97873 -2.22144

7.61991 66.59948

6.35683 35.62167

4.60624 15.37388

What is the correlation?

A. -0.991

B. -0.008

C. 0.984

D. None of the answer are correct

E. 0.310

24.The equation of the regression line is Y= a + bX. Match the following symbols to the description

1.Denotes the variable plotted on the horizontal axis is called the explanatory or independent variable

2.Denotes the variable plotted on the vertical axis and is called the response or dependent variable

3.the regression result = the change in Y for a change in X of +1, and called the slope

4.The proportion of the variability of Y that is explained by the accountable to X

5.The strength and direction of the linear relationship between X and Y

6.The regression result = elevation of the line at X=0, and called the intercept

A. a

B. R

C. b

D. X

E. R²

F. Y

Regression-Assumptions

25.You are required to setup a predictive equation involving variable 1 and variable 2. First plot the data below to determine if linear regression applies

variable1 variable2

5.92418 16.01040

-2.15342 6.90096

-5.68710 3.20965

-2.35173 8.11837

9.13267 20.86393

8.84593 17.88436

0.60205 11.33976

4.30225 13.72104

-9.69073 0.22652

-6.81619 2.88607

7.00841 14.48358

4.48845 15.56499

3.06470 11.36857

-9.46731 1.14076

1.54090 12.95229

-4.20144 5.79307

6.11798 15.91570

9.94412 16.96745

1.32124 10.86254

-7.69106 1.10462

5.89874 15.93450

-0.72913 10.47150

8.39173 17.99690

-9.46846 0.72233

You decide:

A. You need more information before deciding to use linear regression

B. the linear regression equation will be very useful because the points have a strong linear pattern

C. linear regression is not useful because the points have no discernible pattern

D. linear regression is not applicable because the point pattern is curvilinear (has a curve)

E. linear regression is not applicable because it appears that there are two linear patterns indicating that the data comes from two populations

Regression-Interception

26.An important application of regression in manufacturing is the estimation of cost of production. Based on the data below from AJAX widgets relating cost (Y) to volume (X), what is the cost per widget?

Production Volume (units) Total Cost ($)

400 4688

450 4893

550 5957

600 6105

700 7111

750 7743

425 4983

475 5461

575 6136

625 6302

725 7538

775 7596

A. 8.75

B. 7.54

C. 8.21

D. None of the answers are correct

E. 7.38

HINT: What is the regression equation? What do the regression constants mean? 1 widget is a production volume of 1

Regression-Estimate

27.An important application of regression in manufacturing is the estimation of cost of production. Based on the data below from AJAX widgets relating cost (Y) to volume (X), what is the cost of producing 600 widgets?

Production Volume (units) Total Cost ($)

400 5424

450 5657

550 5759

600 7294

700 7583

750 8603

425 5311

475 6093

575 6662

625 7380

725 7784

775 8588

A. 6954

B. 5206

C. 5826

D. None of the answers are correct

E. 6312