Deck 11: Analysis of Variance and Design of Experiments

Question 1

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

Answer 1

False

Question 2

In an experimental design, classification variables are independent variables.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

In an 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.

Question 5

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

Question 6

An experimental design where two or more treatments are considered simultaneously is called a factorial design.

Question 7

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

Question 8

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

Question 9

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

Question 10

A pet adoption agency is considering the probability of a pet being adopted when considering its age and its size.A factorial design can help the agency consider the interaction effects between adoption and size.

Question 11

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.

Question 12

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

Question 13

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

Question 14

An experimental design contains only independent variables.

Question 15

If 5 groups are tested two at a time, the total number of paired comparisons is 9.

Question 16

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 23.50 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.

Question 17

In an experimental design, treatment variables are response variables.

Question 18

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

Question 19

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

Question 20

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.

Question 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.Analysis of Kathleen's data yielded the following ANOVA table. $$\begin{array} { | l | r | r | r | r | } \hline \text { Source of Variation } & { \text { SS } } & { \text { df } } & { \text { MS } } & { \text { F } } \\\hline \text { Treatment } & 33476.19 & 2 & 16738.1 & 9.457912 \\\hline \text { Error } & 26546.18 & 15 & 1769.745 & \\\hline \text { Total } & 60022.37 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the observed F value is _____________.

A)16738.1
B)1769.75
C)33476.19
D)26546.18
E)9.457912

Question 22

Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine the most effective advertisement strategy 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 where 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

Question 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.Analysis of Kathleen's data yielded the following ANOVA table. $$\begin{array} { | l | r | r | r | r | } \hline \text { Source of Variation } & { \text { SS } } & { \text { df } } & { \text { MS } } &{ \text { F } } \\\hline \text { Treatment } & 33476.19 & 2 & 16738.1 & 9.457912 \\\hline \text { Error } & 26546.18 & 15 & 1769.745 & \\\hline \text { Total } & 60022.37 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the critical F value is _____________.

A)13.68
B)19.43
C)3.59
D)19.45
E)3.68

Question 24

In an experimental design, part of the total ___________ in the dependent variable is being explained by differences in the __________ variable.

A)width, key
B)variance, key
C)mean, independent
D)variance, independent
E)width, dependent

Question 25

A college administrator might want to determine if there are differences in credit hour loads based on student living arrangements as well as student grade level.In this case, the dependent variable(s)is/are _________________.

A)credit hours
B)credit hours and living arrangements
C)living arrangements
D)grade level
E)living arrangements and grade level

Question 26

The subcategories of independent variables are often called __________.

A)Levels
B)Dependents
C)ANOVA
D)Experiments
E)Climates

Question 27

Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine the most effective advertisement strategy 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 where they saw the advertisement.In this experiment, the independent variable has how many levels?

A)1
B)2
C)3
D)4
E)0

Question 28

In a two-way ANOVA test, three sets of hypotheses are tested simultaneously.

Question 29

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) $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃
B) $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃
C) $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$ $\mu$ ₃
D) $\mu$ ₁ $\le$ $\mu$ ₂ $\le$$\mu$ ₃
E) $\mu$ ₁ $\le$ $\mu$ ₂ ≥ $\mu$ ₃

Question 30

Which of the following would be an appropriate way for a researcher to use temperature as a classification variable?

A)Increasing the room temperature each hour
B)Selecting individuals from different climates
C)Decreasing the room temperature each hour
D)Selecting individuals based on whether they are wearing coats
E)Changing the density of people in a set area

Question 31

The ANOVA statistical technique is primarily used to determine why there are differences from item to item in the sample when looking at a key variable's _______.

A)variance
B)median
C)mean
D)standard deviation
E)width

Question 32

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)randomized block design
C)normalized block design
D)completely randomized design
E)fractional design

Question 33

Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine the most effective advertisement strategy 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 where 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

Question 34

Which of the following factors would be considered a classification variable?

A)Diets
B)Exercise routines
C)Heights
D)Temperatures in the room
E)Exercise time

Question 35

A college administrator might want to determine if there are differences in credit hour loads based on student living arrangements as well as student grade level.In this case, the independent variable(s)is/are _________________.

A)credit hours
B)credit hours and living arrangements
C)living arrangements
D)grade level
E)living arrangements and grade level

Question 36

Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine the most effective advertisement strategy 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 where 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

Question 37

Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine with method of transportation customers prefer to arrive at the bed and breakfast.In this experiment, they will ask customers how they traveled as well as their satisfaction with that mode of transportation.In this study, the independent variable is a ___________.

A)treatment variable
B)classification variable
C)experimental variable
D)design variable
E)research variable

Question 38

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

Question 39

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

Question 40

When considering the interaction effects, the null hypothesis is that those effects are zero.

Question 41

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

A)factorial design
B)randomized block design
C)completely randomized design
D)normalized block design
E)partially randomized design

Question 42

Cindy Ho, VP of Finance at Discrete Components, Inc.(DCI), theorizes that the discount rate offered to credit customers affects the average collection period on credit sales.Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%)by randomly assigning five customers to each sales discount rate.An analysis of Cindy's data produced the following ANOVA table. $$\begin{array} { | r | r | r | r | r | } \hline \text { Source of Variation } & \mathrm { SS } & \mathrm { df } & \mathrm { MS } & \mathrm { F } \\\hline \text { Treatrnent } & 1844.2 & \mathbf { 3 } & 614.7333 & 7.568277 \\\hline \text { Error } & 1299.6 & 16 & 81.225 & \\\hline \text { Total } & 3143.8 & 19 & & \\\hline\end{array}$$ Using $\alpha$ = 0.01, the appropriate decision is _________.

A)reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄
B)reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$$\mu$ ₃ $\neq$$\mu$ ₄
C)do not reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄= $\mu$ ₅
D)do not reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$$\mu$ ₃ $\neq$$\mu$ ₄ $\neq$ $\mu$ ₅
E)do nothing

Question 43

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. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatment } & 3608.333 & 2 & 1804.167 & \\\hline \text { Errar } & 13591.67 & 15 & 906.1111 & \\\hline \text { Total } & 17200 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the appropriate decision is _____________.

A)do not reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$$\mu$ ₃
B)do not reject the null hypothesis $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃
C)reject the null hypothesis $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$$\mu$ ₃
D)reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$ $\mu$ ₃
E)inclusive

Question 44

BigShots, Inc.is a specialty e-tailer that operates 87 catalog websites on the Internet.Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.)of a website may affect its sales.He chooses three levels of design style (neon, old world and sophisticated)and randomly assigns six catalog websites to each design style.Analysis of Kevin's data yielded the following ANOVA table. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Between Groups } & 384.3333 & 2 & 192.1667 & \\\hline \text { Within Groups } & 1359.667 & 15 & 90.64444 & \\\hline \text { Total } & 1744 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the appropriate decision is _____________.

A)do not reject the null hypothesis $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃
B)do not reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$$\mu$ ₃
C)reject the null hypothesis $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$ $\mu$ ₃
D)reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$ $\mu$ ₃
E)do nothing

Question 45

Cindy Ho, VP of Finance at Discrete Components, Inc.(DCI), theorizes that the discount rate offered to credit customers affects the average collection period on credit sales.Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%)by randomly assigning five customers to each sales discount rate.In Cindy's experiment, "sales discount rate" is ______.

A)the dependent variable
B)a treatment variable
C)a blocking variable
D)a concomitant variable
E)a constant

Question 46

BigShots, Inc.is a specialty e-tailer that operates 87 catalog websites on the Internet.Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.)of a website may affect its sales.He chooses three levels of design style (neon, old world and sophisticated)and randomly assigns six catalog websites to each design style.Analysis of Kevin's data yielded the following ANOVA table. $$\begin{array} { | l | r | r | l | l | } \hline \text { Source of Variation } & \text { SS } & \mathrm { df } & \mathrm { MS } & F \\\hline \text { Between Groups } & 68102.33 & 2 & 34051.17 & 17.50545 \\\hline \text { Within Groups } & 29177.67 & 15 & 1945.178 & \\\hline \text { Total } & 97280 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the appropriate decision is _____________.

A)inconclusive
B)reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$$\mu$ ₃
C)reject the null hypothesis $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃
D)do not reject the null hypothesis $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$ $\mu$ ₃
E)do not reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$ $\mu$ ₃

Question 47

Suppose a researcher sets up a design in which there are five different treatments and a total of 32 measurements in the study.For alpha = .01, the critical table F value is ____.

A)3.75
B)3.78
C)4.07
D)4.11
E)4.91

Question 48

Data from a completely randomized design are shown in the following table. $$\begin{array}{l}\text { Treatment Level }\\\begin{array} { | c | c | c | } \hline 1 & 2 & 3 \\\hline 27 & 26 & 27 \\\hline 26 & 22 & 29 \\\hline 23 & 21 & 27 \\\hline 24 & 23 & 26 \\\hline\end{array}\end{array}$$ For a one-way ANOVA, the Total Sum of Squares (SST)is ________.

A)36.17
B)28.75
C)64.92
D)18.03
E)28.04

Question 49

Cindy Ho, VP of Finance at Discrete Components, Inc.(DCI), theorizes that the discount rate offered to credit customers affects the average collection period on credit sales.Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%)by randomly assigning five customers to each sales discount rate.In Cindy's experiment, "average collection period" is ________.

A)the dependent variable
B)a treatment variable
C)a blocking variable
D)a concomitant variable
E)a constant

Question 50

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

A) $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$ $\mu$ ₃
B) $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃
C) $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃
D) $\mu$ ₁ $\le$ $\mu$ ₂ $\le$ $\mu$ ₃
E) $\mu$ ₁ $\le$ $\mu$ ₂ ≥ $\mu$ ₃

Question 51

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. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatment } & 3608.333 & 2 & 1804.167 & \\\hline \text { Errar } & 13591.67 & 15 & 906.1111 & \\\hline \text { Total } & 17200 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the critical F value is _____________.

A)13.68
B)19.43
C)3.59
D)19.45
E)3.68

Question 52

BigShots, Inc.is a specialty e-tailer that operates 87 catalog websites on the Internet.Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.)of a website may affect its sales.He chooses three levels of design style (neon, old world and sophisticated)and randomly assigns six catalog websites to each design style.Analysis of Kevin's data yielded the following ANOVA table. $$\begin{array} { | l | r | r | l | l | } \hline \text { Source of Variation } & \text { SS } & \mathrm { df } & \mathrm { MS } & \boldsymbol { F } \\\hline \text { Between Groups } & 68102.33 & 2 & 34051.17 & \\\hline \text { Within Groups } & 29177.67 & 15 & 1945.178 & \\\hline \text { Total } & 97280 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the critical F value is _____________.

A)3.57
B)19.43
C)3.68
D)19.45
E)2.85

Question 53

BigShots, Inc.is a specialty e-tailer that operates 87 catalog websites on the Internet.Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.)of a website may affect its sales.He chooses three levels of design style (neon, old world and sophisticated)and randomly assigns six catalog websites to each design style.Analysis of Kevin's data yielded the following ANOVA table. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Between Groups } & 68102.33 & 2 & 34051.17 & \\\hline \text { Within Groups } & 29177.67 & 15 & 1945.178 & \\\hline \text { Total } & 97280 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the observed F value is _____________.

A)0.5022
B)0.1333
C)1.9911
D)17.5100
E)22.4567

Question 54

Cindy Ho, VP of Finance at Discrete Components, Inc.(DCI), theorizes that the discount rate offered to credit customers affects the average collection period on credit sales.Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%)by randomly assigning five customers to each sales discount rate.An analysis of Cindy's data produced the following ANOVA table. $$\begin{array} { | r | r | r | r | r | } \hline \text { Source of Variation } & \mathbf { S S } & \mathrm { df } & \mathrm { MS } & \text { F } \\\hline \text { Treatrnent } & 5.35 & \mathbf { 3 } & 1.783333 & \\\hline \text { Error } & 177.2 & 16 & 11.075 & \\\hline \text { Total } & 182.55 & 19 & & \\\hline\end{array}$$ Using $\alpha$ = 0.01, the observed F value is _________.

A)6.2102
B)0.1610
C)0.1875
D)5.3333
E)4.9873

Question 55

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. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatment } & 3608.333 & 2 & 1804.167 & \\\hline \text { Errar } & 13591.67 & 15 & 906.1111 & \\\hline \text { Total } & 17200 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the observed F value is _____________.

A)0.5022
B)0.1333
C)1.9911
D)7.5000
E)1.000

Question 56

Cindy Ho, VP of Finance at Discrete Components, Inc.(DCI), theorizes that the discount rate offered to credit customers affects the average collection period on credit sales.Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%)by randomly assigning five customers to each sales discount rate.An analysis of Cindy's data produced the following ANOVA table. $$\begin{array} { | r | r | r | r | r | } \hline \text { Source of Variation } & \mathbf { S S } & \mathrm { df } & \mathrm { MS } & \text { F } \\\hline \text { Treatrnent } & 5.35 & \mathbf { 3 } & 1.783333 & \\\hline \text { Error } & 177.2 & 16 & 11.075 & \\\hline \text { Total } & 182.55 & 19 & & \\\hline\end{array}$$ Using $\alpha$ = 0.01, the critical F value is _________.

A)5.33
B)6.21
C)0.16
D)5.29
E)6.89

Question 57

Cindy Ho, VP of Finance at Discrete Components, Inc.(DCI), theorizes that the discount rate offered to credit customers affects the average collection period on credit sales.Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%)by randomly assigning five customers to each sales discount rate.An analysis of Cindy's data produced the following ANOVA table. $$\begin{array} { | r | r | r | r | r | } \hline \text { Source of Variation } & \mathbf { S S } & \mathrm { df } & \mathrm { MS } & \text { F } \\\hline \text { Treatrnent } & 5.35 & \mathbf { 3 } & 1.783333 & \\\hline \text { Error } & 177.2 & 16 & 11.075 & \\\hline \text { Total } & 182.55 & 19 & & \\\hline\end{array}$$ Using $\alpha$ = 0.01, the appropriate decision is _________.

A)reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄
B)reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$$\mu$ ₃ $\neq$$\mu$ ₄
C)do not reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄
D)do not reject the null hypothesis $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃ $\neq$$\mu$ ₄
E)do nothing

Question 58

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. $$\begin{array} { | l | r | r | r | r | } \hline \text { Source of Variation } & { \text { SS } } & { \text { df } } & { \text { MS } } & { \text { F } } \\\hline \text { Treatment } & 33476.19 & 2 & 16738.1 & 9.457912 \\\hline \text { Error } & 26546.18 & 15 & 1769.745 & \\\hline \text { Total } & 60022.37 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the appropriate decision is _____________.

A)reject the null hypothesis $\mu$ ₁ = $\mu$ ₂= $\mu$ ₃
B)reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃
C)do not reject the null hypothesis $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$ $\mu$ ₃
D)do not reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$ $\mu$ ₃
E)inconclusive

Question 59

Cindy Ho, VP of Finance at Discrete Components, Inc.(DCI), theorizes that the discount rate offered to credit customers affects the average collection period on credit sales.Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%)by randomly assigning five customers to each sales discount rate.Cindy's experimental design is a ________.

A)factorial design
B)randomized block design
C)completely randomized design
D)normalized block design
E)incomplete block design

Question 60

Cindy Ho, VP of Finance at Discrete Components, Inc.(DCI), theorizes that the discount rate offered to credit customers affects the average collection period on credit sales.Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%)by randomly assigning five customers to each sales discount rate.Cindy's null hypothesis is ______.

A) $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃ = $\mu$ ₄ = $\mu$ ₅
B) $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃ $\neq$$\mu$ ₄ $\neq$$\mu$ ₅
C) $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$$\mu$ ₃ $\neq$$\mu$ ₄
D) $\mu$ ₁ = $\mu$ ₂ = $\mu$ ₃ = $\mu$ ₄
E) $\mu$ ₁ ≠ $\mu$ ₂ = $\mu$ ₃ = $\mu$ ₄

Question 61

For the following ANOVA table, the observed F value is ___________. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \mathrm { df } & \text { MS } & F \\\hline \text { Treatment } & 150 & & & \\\hline \text { Error } & 40 & 20 & & \\\hline \text { Total } & & 23 & & \\\hline\end{array}$$

A)0.5625
B)50
C)25
D)0.02
E)0.09

Question 62

For the following ANOVA table, the df_Treatment value is ___________. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatrnent } & 150 & & & \\\hline \text { Error } & 40 & 20 & & \\\hline \text { Total } & & 23 & & \\\hline\end{array}$$

A)3
B)43
C)1.15
D)460
E)150

Question 63

For the following ANOVA table, the HSD value, assuming equal sample sizes and using $\alpha$ = 0.01, is ______. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatrnent } & 0.1233 & 2 & 0.06165 & 1.566311 \\\hline \text { Error } & 0.5904 & 15 & 0.03936 & \\\hline \text { Total } & 0.7137 & 17 & & \\\hline\end{array}$$

A)0.39
B)0.55
C)0.48
D)0.43
E)0.68

Question 64

If the confidence interval for the difference of means contains zero, then it can be concluded that ________________.

A)there is a significant difference in the variances
B)there is not a significant difference in the means
C)there is a significant difference in the means
D)the groups are the same on all measures
E)there is not a significant difference in the variances

Question 65

The results of an experiment comparing the cycle lengths of three different brands of washing machines (N=33)indicated an overall mean square error of 2.58.The researcher believes that the brands 1 and 2 may be the most different as they have mean cycles of 31.8 (n=12)and 35.9 (n=10).Using an alpha of 0.05, what would be the q obtained for this problem?

A)3.44
B)3.80
C)2.86
D)3.49
E)3.82

Question 66

For the following ANOVA table, the HSD value, assuming equal sample sizes and using $\alpha$ = 0.05 is ______. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatment } & 36.17 & 2 & 18.08 & 5.66 \\\hline \text { Error } & 28.75 & 9 & 3.19 & \\\hline \text { Total } & 64.92 & 11 & & \\\hline\end{array}$$

A)1.86
B)3.94
C)3.19
D)1.645
E)3.52

Question 67

Data from a completely randomized design are shown in the following table. $$\begin{array}{l}\text { Treatment Level }\\\begin{array} { | c | c | c | } \hline 1 & 2 & 3 \\\hline 27 & 26 & 27 \\\hline 26 & 22 & 29 \\\hline 23 & 21 & 27 \\\hline 24 & 23 & 26 \\\hline\end{array}\end{array}$$ For a one-way ANOVA using $\alpha$ = 0.05, the critical F value is ________.

A)3.86
B)3.59
C)19.38
D)4.26
E)6.8

Question 68

For the following ANOVA table, the MS Error value is ___________. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \mathrm { df } & \text { MS } & F \\\hline \text { Treatment } & 150 & & & \\\hline \text { Error } & 40 & 20 & & \\\hline \text { Total } & & 23 & & \\\hline\end{array}$$

A)20
B)60
C)800
D)2
E)200

Question 69

For the following ANOVA table, the MS Error value is ___________. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \mathrm { df } & \text { MS } & F \\\hline \text { Treatment } & & 4 & & \\\hline \text { Error } & 360 & & & \\\hline \text { Total } & 440 & 16 & & \\\hline\end{array}$$

A)4,320
B)372
C)348
D)30
E)4

Question 70

Data from a completely randomized design are shown in the following table. $$\begin{array}{l}\text { Treatment Level }\\\begin{array} { | c | c | c | } \hline 1 & 2 & 3 \\\hline 27 & 26 & 27 \\\hline 26 & 22 & 29 \\\hline 23 & 21 & 27 \\\hline 24 & 23 & 26 \\\hline\end{array}\end{array}$$ For a one-way ANOVA using $\alpha$ = 0.05, the appropriate decision is ________.

A)do not reject the null hypothesis $\mu$ ₁ $\ge$$\mu$ ₂ $\ge$$\mu$ ₃
B)do not reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$$\mu$ ₃
C)reject the null hypothesis $\mu$ ₁= $\mu$ ₂= $\mu$ ₃
D)reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃
E)do not reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ 0 $\mu$ ₃

Question 71

Posteriori pairwise comparisons are only made in situations where ______________.

A)there was a significant F value and it is after the experiment
B)there was not a significant F value and it is after the experiment
C)there was a significant F value and it is before the experiment
D)the analyst wants to compare any two samples after the experiment
E)there was not a significant F value and it is before the experiment

Question 72

For the following ANOVA table, the critical value of the studentized range distribution using $\alpha$ = 0.01 is ______. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatrnent } & 0.1233 & 2 & 0.06165 & 1.566311 \\\hline \text { Error } & 0.5904 & 15 & 0.03936 & \\\hline \text { Total } & 0.7137 & 17 & & \\\hline\end{array}$$

A)3.01
B)3.67
C)4.17
D)4.83
E)5.25

Question 73

For the following ANOVA table, the MS Treatment value is ___________. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatment } & & 4 & & \\\hline \text { Error } & 360 & & & \\\hline \text { Total } & 440 & 16 & & \\\hline\end{array}$$

A)20
B)200
C)76
D)84
E)360

Question 74

Data from a completely randomized design are shown in the following table. $$\begin{array}{l}\text { Treatment Level }\\\begin{array} { | c | c | c | } \hline 1 & 2 & 3 \\\hline 27 & 26 & 27 \\\hline 26 & 22 & 29 \\\hline 23 & 21 & 27 \\\hline 24 & 23 & 26 \\\hline\end{array}\end{array}$$ For a one-way ANOVA, the Between Sum of Squares (SSC is ________.

A)36.17
B)28.75
C)64.92
D)18.03
E)28.04

Question 75

Data from a completely randomized design are shown in the following table. $$\begin{array}{l}\text { Treatment Level }\\\begin{array} { | c | c | c | } \hline 1 & 2 & 3 \\\hline 27 & 26 & 27 \\\hline 26 & 22 & 29 \\\hline 23 & 21 & 27 \\\hline 24 & 23 & 26 \\\hline\end{array}\end{array}$$ For a one-way ANOVA, the Error Sum of Squares (SSE)is ________.

A)36.17
B)28.75
C)64.92
D)18.03
E)28.04

Question 76

Data from a completely randomized design are shown in the following table. $$\begin{array}{l}\text { Treatment Level }\\\begin{array} { | c | c | c | } \hline 1 & 2 & 3 \\\hline 27 & 26 & 27 \\\hline 26 & 22 & 29 \\\hline 23 & 21 & 27 \\\hline 24 & 23 & 26 \\\hline\end{array}\end{array}$$ For a one-way ANOVA using $\alpha$ = 0.05, the observed F value is ________.

A)5.66
B)3.19
C)18.08
D)4.34
E)8.98

Question 77

For the following ANOVA table, the critical value of the studentized range distribution using $\alpha$ = 0.05 is ______. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatment } & 36.17 & 2 & 18.08 & 5.66 \\\hline \text { Error } & 28.75 & 9 & 3.19 & \\\hline \text { Total } & 64.92 & 11 & & \\\hline\end{array}$$

A)1.86
B)3.95
C)9.17
D)1.65
E)1.79

Question 78

For the following ANOVA table, the observed F value is ___________. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \mathrm { df } & \text { MS } & F \\\hline \text { Treatment } & & 4 & & \\\hline \text { Error } & 360 & & & \\\hline \text { Total } & 440 & 16 & & \\\hline\end{array}$$

A)0.67
B)1.50
C)6.00
D)5.00
E)4.00

Question 79

For the following ANOVA table, the df_Error value is ___________. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatment } & & 4 & & \\\hline \text { Error } & 360 & & & \\\hline \text { Total } & 440 & 16 & & \\\hline\end{array}$$

A)4
B)20
C)12
D)64
E)16

Question 80

For the following ANOVA table, the MS Treatment value is ___________. $$\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & \text { SS } & \text { df } & \text { MS } & F \\\hline \text { Treatment } & 150 & & & \\\hline \text { Error } & 40 & 20 & & \\\hline \text { Total } & & 23 & & \\\hline\end{array}$$

A)150
B)50
C)450
D)3.49
E)40