Analysis of Variance and Design of Experiments True/False and Multiple Choice

Analysis of Variance and Design of Experiments

True/False

1. In experimental design, classification variables are independent variables.

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables—both treatment and classification—and dependent variables.

2. In an experimental design, treatment variables are response variables.

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables—both treatment and classification—and dependent variables.

3. In experimental design, a characteristic of the subjects that was present prior to the experiment and is not the result of the experimenter’s manipulations or control is called a classification variable.

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables—both treatment and classification—and dependent variables.

4. In experimental design, a variable that the experimenter controls or modifies in the experiment is called a treatment variable.

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables—both treatment and classification—and dependent variables.

5. An experimental design contains only independent variables.

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables—both treatment and classification—and dependent variables.

6. Analysis of variance may be used to test the differences in the means of more than two independent populations.

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA) Difficulty: Difficulty: Easy

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

7. In analysis of variance tests a F distribution forms the basis for making the decisions.

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA) Difficulty: Difficulty: Easy

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

8. The statistical methods of analysis of variance assume that the populations are normally distributed.

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA) Difficulty: Difficulty: Easy

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

9. The statistical methods of analysis of variance assume equal sample means.

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA) Difficulty: Difficulty: Easy

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

10. Determining the table value for the F distribution requires two values for degrees of freedom.

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA) Difficulty: Difficulty: Easy

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

11. The Tukey-Kramer procedure is based on construction of confidence intervals for each pair of treatment means at a time.

Ans:

Response: See section 11.3 Multiple Comparison Tests

Difficulty: Medium

Learning Objective: 11.3: Use multiple comparison techniques, including Tukey’s honestly significant difference test and the Tukey-Kramer procedure, to test the difference in two treatment means when there is overall significant difference between treatments.

12. The Tukey-Kramer procedure allows us to simultaneously examine all pairs of population means after the ANOVA test has been completed without increasing the true α level.

Ans:

Response: See section 11.3 Multiple Comparison Tests

Difficulty: Medium

Learning Objective: 11.3: Use multiple comparison techniques, including Tukey’s honestly significant difference test and the Tukey-Kramer procedure, to test the difference in two treatment means when there is overall significant difference between treatments.

13. A completely randomized design has been analyzed by using a one-way ANOVA. There are three treatment groups in the design, and each sample size is four. The mean for group 1 is 25.00 and for group 3 it is 27.50. MSE is 3.19. Using α=0.05 there is a significant difference between these two groups.

Ans:

Response: See section 11.3 Multiple Comparison Tests

Difficulty: Hard

Learning Objective: 11.3: Use multiple comparison techniques, including Tukey’s honestly significant difference test and the Tukey-Kramer procedure, to test the difference in two treatment means when there is overall significant difference between treatments.

14. In a randomized complete block design the conclusion might be that blocking is not necessary.

Ans:

Response: See section 11.4 The Randomized Block Design

Difficulty: Easy

Learning Objective: 11.4: Test a randomized block design which includes a blocking variable to control for confounding variables.

15. The F value for treatment will always increase if we include a blocking effect.

Ans:

Response: See section 11.4 The Randomized Block Design

Difficulty: Easy

Learning Objective: 11.4: Test a randomized block design which includes a blocking variable to control for confounding variables.

16. Interaction effects in a factorial design can be analyzed in randomized block design.

Ans:

Response: See section 11.5 Factorial Design (Two-Way ANOVA)

Difficulty: Easy

Learning Objective: 11.5: Test a factorial design using a two-way analysis of variance, noting the advantages and applications of such a design and accounting for possible interaction between two treatment variables.

Multiple Choice

17. Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine effective advertisement strategies for increasing the number of reservations. The bed and breakfast owners intend to rotate advertisements for 12 weeks between a travel website, a travel magazine and a local billboard. Customers making reservations will be asked if they saw the advertisement. In this experiment, the dependent variable is ________________.

a. advertisement venue

b. bed and breakfast establishment

c. travel website

d. number of reservations

e. number of customer calls

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables – both treatment and classification – and dependent variables.

18. Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine effective advertisement strategies for increasing the number of reservations. The bed and breakfast owners intend to rotate advertisements for 12 weeks between a travel website, a travel magazine and a local billboard. Customers making reservations will be asked if they saw the advertisement. In this experiment, the independent variable is ________________.

a. advertisement venue

b. bed and breakfast establishment

c. travel website

d. number of reservations

e. number of customer calls

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables – both treatment and classification – and dependent variables.

19. Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine effective advertisement strategies for increasing the number of reservations. The bed and breakfast owners intend to rotate advertisements for 12 weeks between a travel website, a travel magazine and a local billboard. Customers making reservations will be asked if they saw the advertisement. In this experiment, the independent variable has how many levels?

a. 1

b. 2

c. 3

d. 4

e. 0

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables – both treatment and classification – and dependent variables.

20. Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine effective advertisement strategies for increasing the number of reservations. The bed and breakfast owners intend to rotate advertisements for 12 weeks between a travel website, a travel magazine and a local billboard. Customers making reservations will be asked if they saw the advertisement. In this experiment, the independent variable is a ________________.

a. treatment variable

b. classification variable

c. experimental variable

d. design variable

e. research variable

Ans:

Response: See section 11.1 Introduction to Design of Experiments

Difficulty: Easy

Learning Objective: 11.1: Describe an experimental design and its elements, including independent variables – both treatment and classification – and dependent variables.

21. Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children’s cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Kathleen’s experimental design is a ________.

a) factorial design

b) random block design

c) normalized block design

d) completely randomized design

e) fractional design

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA) Difficulty: Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

22.          Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children’s cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. In Kathleen’s experimental design “painting style” is _______.

a) the dependent variable

b) a concomitant variable

c) a treatment variable

d) a blocking variable

e) a response variable

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA) Difficulty: Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

23.          Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children’s cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. In Kathleen’s experimental design “reduced length of stay” is _______.

a) the dependent variable

b) a concomitant variable

c) a treatment variable

d) a blocking variable

e) a constant

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA) Difficulty: Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

24.          Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children’s cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Kathleen’s null hypothesis is _____________.

a)  1   2   3

b)  1   2   3

c)  1   2   3

d)  1   2   3

e)  1   2 ≥  3

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Easy

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

25.          Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children’s cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Analysis of Kathleen’s data yielded the following ANOVA table.

Source of Variation         SS           df            MS         F

Treatment          33476.19              2              16738.1 9.457912

Error      26546.18              15           1769.745             

Total      60022.37              17                          

Using  = 0.05, the critical F value is _____________.

a) 13.68

b) 19.43

c) 3.59

d) 19.45

e) 3.68

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

26.          Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children’s cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Analysis of Kathleen’s data yielded the following ANOVA table.

Source of Variation         SS           df            MS         F

Treatment          33476.19              2              16738.1 9.457912

Error      26546.18              15           1769.745             

Total      60022.37              17                          

Using  = 0.05, the observed F value is _____________.

a) 16738.1

b) 1769.75

c) 33476.19

d) 26546.18

e) 9.457912

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

27.          Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children’s cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Analysis of Kathleen’s data yielded the following ANOVA table.

Source of Variation         SS           df            MS         F

Treatment          33476.19              2              16738.1 9.457912

Error      26546.18              15           1769.745             

Total      60022.37              17                          

Using  = 0.05, the appropriate decision is _____________.

a) reject the null hypothesis  1   2  3

b) reject the null hypothesis  1   2   3

c) do not reject the null hypothesis  1   2   3

d) do not reject the null hypothesis  1   2   3

e) inconclusive

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

28.          Pate’s Pharmacy, Inc. operates a regional chain of 120 pharmacies.  Each pharmacy’s floor plan includes a greeting card department which is relatively isolated.  Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department.  She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level.  Analysis of Sandra’s data yielded the following ANOVA table. 

Source of Variation         SS           df            MS         F

Treatment          3608.333              2              1804.167             

Error      13591.67              15           906.1111             

Total      17200    17                          

Using  = 0.05, the critical F value is _____________.

a) 13.68

b) 19.43

c) 3.59

d) 19.45

e) 3.68

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

29.          Pate’s Pharmacy, Inc. operates a regional chain of 120 pharmacies.  Each pharmacy’s floor plan includes a greeting card department which is relatively isolated.  Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department. She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level.  Analysis of Sandra’s data yielded the following ANOVA table. 

Source of Variation         SS           df            MS         F

Treatment          3608.333              2              1804.167             

Error      13591.67              15           906.1111             

Total      17200    17                          

Using  = 0.05, the observed F value is _____________.

a) 0.5022

b) 0.1333

c) 1.9911

d) 7.5000

e) 1.000

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

30.          Pate’s Pharmacy, Inc. operates a regional chain of 120 pharmacies.  Each pharmacy’s floor plan includes a greeting card department which is relatively isolated.  Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department.  She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level. Analysis of Sandra’s data yielded the following ANOVA table. 

Source of Variation         SS           df            MS         F

Treatment          3608.333              2              1804.167             

Error      13591.67              15           906.1111             

Total      17200    17                          

Using  = 0.05, the appropriate decision is _____________.

a) do not reject the null hypothesis  1   2   3

b) do not reject the null hypothesis  1  2   3

c) reject the null hypothesis  1   2    3

d) reject the null hypothesis  1   2   3

e) inclusive

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

31.          BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet.  Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales.  He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style.  Kevin’s experimental design is a ________.

a) factorial design

b) random block design

c) completely randomized design

d) normalized block design

e) partially randomized design

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

32.          BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet.  Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales.  He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style.  Kevin’s null hypothesis is _____________.

a)  1   2   3

b)  1   2   3

c)  1   2  3

d)  1   2   3

e)  1   2 ≥  3

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

33.          BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet.  Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales.  He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style.  Analysis of Kevin’s data yielded the following ANOVA table. 

Source of Variation         SS           df            MS         F

Between Groups             68102.33              2              34051.17              17.50543

Within Groups   29177.67              15           1945.178             

Total      97280    17                          

Using  = 0.05, the appropriate decision is _____________.

a) inconclusive

b) reject the null hypothesis  1   2   3

c) reject the null hypothesis  1  2   3

d) do not reject the null hypothesis  1   2   3

e) do not reject the null hypothesis  1   2   3

Ans:

Response: See section 11.2 The Completely Randomized Design (One-Way ANOVA)

Difficulty: Medium

Learning Objective: 11.2: Test a completely randomized design using a one-way analysis of variance.

34.          BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet.  Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales.  He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style.  Analysis of Kevin’s data yielded the following ANOVA table. 

Source of Variation         SS           df            MS         F

Between Groups             68102.33              2              34051.17             

Within Groups   29177.67              15           1945.178             

Total      97280    17                          

Using  = 0.05, the critical F value is _____________.

a) 3.57

b) 19.43

c) 3.68

d) 19.45

e) 2.85

Ans:

Response: See section 11.2 The Completely Randomized De

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