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

Data from a randomized block design are shown in the following table. $\begin{array}{c} \quad\quad\quad\text { Treatment Levels }\\ \begin{array}{l} \\ \text {Block 1}\\ \text {Block 2}\\ \text {Block3} \end{array} \begin{array}{l} 1 \\ 8 \\ 6 \\ 7 \end{array} \begin{array}{l} 2 \\ 5 \\ 6 \\ 8 \end{array} \begin{array}{c} 3 \\ 10 \\ 9 \\ 8 \end{array} \begin{array}{r} 4\\ 7\\ 5\\ 9 \end{array} \end{array}$ With $\alpha$ = 0.05, the observed F value for the blocking effects null hypothesis is__.

A) 0.37 B) 5.14 C) 1.17 D) 2.33 E) 2.00 A) 0.37 B) 5.14 C) 1.17 D) 2.33 E) 2.00

At a local community college, the head of the math department is interested in determining the effects of two factors on the final exam performance.The two factors are: (1)whether the student completed all the suggested exercises (yes or no), and (2)how many cups of coffee the student took the morning of the exam (0, 1, or 2).Analysis of the data is summarized in the following ANOVA table: \[\begin{array} { | c | c | c | c | c | } \hline \text { Source of Variation } & 3 \mathrm {~S} & \mathrm { df } & \mathrm { Ms } & F \\ \hline \text { Rows (exercises) } & \mathbf { 2 3 3 4 . 7 2 } & 1 & \mathbf { 2 3 3 4 . 7 2 } & 11.36 \\ \hline \text { Colurnu (coffee) } & 2936.11 & 2 & 1486.06 & 7.14 \\ \hline \text { Irteraction } & 2569.45 & 2 & 1284.73 & 6.25 \\ \hline \text { Withirl } & 2466.66 & 12 & 205.56 & \\ \hline \text { Total } & 10306.94 & 17 & & \\ \hline \end{array}\] Using $\alpha$ = .05, the conclusions are: _____________.

A) a significant effect of completing the exercises but not of drinking coffee and no significant interaction B) a significant effect of drinking coffee but not of completing the exercises and no significant interaction C) a significant effect of both completing the exercises and drinking coffee but no significant interaction D) a significant effect of both completing the exercises and drinking coffee as well as a significant interaction E) no significant effect of completing the exercises or drinking coffee and no significant interaction A) a significant effect of completing the exercises but not of drinking coffee and no significant interaction B) a significant effect of drinking coffee but not of completing the exercises and no significant interaction C) a significant effect of both completing the exercises and drinking coffee but no significant interaction D) a significant effect of both completing the exercises and drinking coffee as well as a significant interaction E) no significant effect of completing the exercises or drinking coffee and no significant interaction

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

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

Exam 11: Analysis of Variance and Design of Experiments

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. Source of Variation SS df MS F Between Groups 384.3333 2 192.1667 Within Groups 1359.667 15 90.64444 Total 1744 17 Using $\alpha$ = 0.05, the appropriate decision is _____________.

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(Multiple Choice)

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Question 1

Correct Answer:

Verified

A

A pet trainer wants to test the effects of "treats" and "voice tone" on the speed with which dogs are trained to roll over.For "treats," the trainer used pieces of hot dogs, biscuits, and bacon flavored treats.For "voice tone," the trainer used sing-song, high pitched, and low pitched.Six dogs were randomly assigned to each of the nine cells and the analysis produced the following ANOVA table. Source of Variation SS F Rows (treats) 3.5926 2 1.79296 0.27 Colurun (voice tone) 14.8148 2 7.40741 1.11 Irteraction 19.1852 4 4.79296 0.72 In this experiment, "voice tone" would be considered _____________.

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(Multiple Choice)

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Question 2

Correct Answer:

Verified

D

A pet trainer wants to test the effects of "treats" and "voice tone" on the speed with which dogs are trained to roll over.For "treats," the trainer used pieces of hot dogs, biscuits, and bacon flavored treats.For "voice tone," the trainer used sing-song, high pitched, and low pitched.Six dogs were randomly assigned to each of the nine cells and the analysis produced the following ANOVA table. Source of Variation SS F Rows (treats) 3.5926 2 1.79296 0.27 Colurun (voice tone) 14.8148 2 7.40741 1.11 Irteraction 19.1852 4 4.79296 0.72 Using $\alpha$ = .05, the appropriate decision for "interaction" effect is that _____________.

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(Multiple Choice)

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Question 3

Correct Answer:

Verified

E

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 _______.

(Multiple Choice)

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Question 4

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

(True/False)

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Question 5

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

(True/False)

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Question 6

Data from a completely randomized design are shown in the following table. Treatment Level 1 2 3 27 26 27 26 22 29 23 21 27 24 23 26 For a one-way ANOVA using $\alpha$ = 0.05, the critical F value is ________.

(Multiple Choice)

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Question 7

A manufacturer of heaters wants to determine if the height of the heater warms a room more quickly.Four different heights were studied.The shortest heater group had n=12 with an average time to heat the room of 15.9 minutes.The tallest heater group had n=10 with an average time to heat the room of 17.3 minutes.Using an alpha of 0.01, MSE of 2.88, and N=44, would the research find evidence of a significant difference in these brands?

(Multiple Choice)

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Question 8

Data from a randomized block design are shown in the following table. Treatment Levels Block 1 Block 2 Block3 1 8 6 7 2 5 6 8 3 10 9 8 4 7 5 9 With $\alpha$ = 0.05, the observed F value for the blocking effects null hypothesis is__.

(Multiple Choice)

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Question 9

While reviewing staffing plans for a new pilot plant, Colin Chenaux, VP of Operations at Clovis Chemicals, Inc., designed an experiment to test the effects of "supervisor's style" and "training method" on the productivity of operators.The treatment levels were: (1)authoritarian, and participatory for supervisor's style, and (2)technical manuals, training films, and multimedia for training method.Three qualified applicants were randomly selected and assigned to each of the six cells.In Colin's experiment, "operator productivity" is _____________.

(Multiple Choice)

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Question 10

At a local community college, the head of the math department is interested in determining the effects of two factors on the final exam performance.The two factors are: (1)whether the student completed all the suggested exercises (yes or no), and (2)how many cups of coffee the student took the morning of the exam (0, 1, or 2).Analysis of the data is summarized in the following ANOVA table: Source of Variation 3 F Rows (exercises) 1 11.36 Colurnu (coffee) 2936.11 2 1486.06 7.14 Irteraction 2569.45 2 1284.73 6.25 Withirl 2466.66 12 205.56 Total 10306.94 17 Using $\alpha$ = .05, the conclusions are: _____________.

(Multiple Choice)

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Question 11

If an experiment had a total of 7 groups, how many pairs of groups could be test with a pairwise comparison?

(Multiple Choice)

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Question 12

A medical researcher is interested in how weight gain in children from third-world countries is affected by the source of protein (fish, roots and tubers, or nuts and oilseeds)and by level of protein intake (low, defined as less than 0.56 grams per kilogram of weight, or high).The researcher wants to test the relative efficacy of each protein source, controlling for the level of protein intake but not testing it as the main variable of interest.For this purpose, she classifies a group of children in an impoverished village in a third-world country into either high or low protein intake.Then, the researcher randomly assigns 50 children from each category to a group where the children will receive food once a day that will emphasize one of the three protein sources.You can assume that the total level of protein intake is not affected (its effects take a longer time to show and depend largely on the other meals the children have at home).The researcher's alternative hypothesis is ______.

(Multiple Choice)

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Question 13

A medical researcher is interested in how weight gain in children from third-world countries is affected by the source of protein (fish, roots and tubers, or nuts and oilseeds)and by level of protein intake (low, defined as less than 0.56 grams per kilogram of weight, or high).The researcher wants to test the relative efficacy of each protein source, controlling for the level of protein intake but not testing it as the main variable of interest.For this purpose, she classifies a group of children in an impoverished village in a third-world country into either high or low protein intake.Then, the researcher randomly assigns 50 children from each category to a group where the children will receive food once a day that will emphasize one of the three protein sources.You can assume that the total level of protein intake is not affected (it's effects take a longer time to show and depend largely on the other meals the children have at home).In this experiment, the level of protein intake is ______.

(Multiple Choice)

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Question 14

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 _______.

(Multiple Choice)

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Question 15

For the following ANOVA table, the critical value of the studentized range distribution using $\alpha$ = 0.01 is ______. Source of Variation SS df MS F Treatrnent 0.1233 2 0.06165 1.566311 Error 0.5904 15 0.03936 Total 0.7137 17

(Multiple Choice)

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Question 16

The following graph indicates a _______________.

(Multiple Choice)

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Question 17

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. Source of Variation F Treatrnent 5.35 1.783333 Error 177.2 16 11.075 Total 182.55 19 Using $\alpha$ = 0.01, the appropriate decision is _________.

(Multiple Choice)

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Question 18

While reviewing staffing plans for a new pilot plant, Colin Chenaux, VP of Operations at Clovis Chemicals, Inc., designed an experiment to test the effects of "supervisor's style" and "training method" on the productivity of operators.The treatment levels were: (1)authoritarian, and participatory for supervisor's style, and (2)technical manuals, training films, and multimedia for training method.Three qualified applicants were randomly selected and assigned to each of the six cells.In Colin's experiment, "training method" is _____________.

(Multiple Choice)

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Question 19

Data from a completely randomized design are shown in the following table. Treatment Level 1 2 3 27 26 27 26 22 29 23 21 27 24 23 26 For a one-way ANOVA using $\alpha$ = 0.05, the observed F value is ________.

(Multiple Choice)

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Question 20

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 _______.

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

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

Data from a completely randomized design are shown in the following table. Treatment Level 1 2 3 27 26 27 26 22 29 23 21 27 24 23 26 For a one-way ANOVA using $\alpha$ = 0.05, the critical F value is ________.

Data from a randomized block design are shown in the following table. Treatment Levels Block 1 Block 2 Block3 1 8 6 7 2 5 6 8 3 10 9 8 4 7 5 9 With $\alpha$ = 0.05, the observed F value for the blocking effects null hypothesis is__.

If an experiment had a total of 7 groups, how many pairs of groups could be test with a pairwise comparison?

For the following ANOVA table, the critical value of the studentized range distribution using $\alpha$ = 0.01 is ______. Source of Variation SS df MS F Treatrnent 0.1233 2 0.06165 1.566311 Error 0.5904 15 0.03936 Total 0.7137 17

The following graph indicates a _______________.

Data from a completely randomized design are shown in the following table. Treatment Level 1 2 3 27 26 27 26 22 29 23 21 27 24 23 26 For a one-way ANOVA using $\alpha$ = 0.05, the observed F value is ________.

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Probability

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Building Multiple Regression Models

Time-Series Forecasting and Index Numbers

Analysis of Categorical Data

Nonparametric Statistics

Statistical Quality Control

Decision Analysis

Filters

Exam 11: Analysis of Variance and Design of Experiments

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 _______.

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

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

Data from a completely randomized design are shown in the following table. Treatment Level 1 2 3 27 26 27 26 22 29 23 21 27 24 23 26 For a one-way ANOVA using α\alphaα = 0.05, the critical F value is ________.

Data from a randomized block design are shown in the following table. Treatment Levels Block 1 Block 2 Block3 1 8 6 7 2 5 6 8 3 10 9 8 4 7 5 9 With α\alphaα = 0.05, the observed F value for the blocking effects null hypothesis is__.

If an experiment had a total of 7 groups, how many pairs of groups could be test with a pairwise comparison?

For the following ANOVA table, the critical value of the studentized range distribution using α\alphaα = 0.01 is ______. Source of Variation SS df MS F Treatrnent 0.1233 2 0.06165 1.566311 Error 0.5904 15 0.03936 Total 0.7137 17

The following graph indicates a _______________.

Data from a completely randomized design are shown in the following table. Treatment Level 1 2 3 27 26 27 26 22 29 23 21 27 24 23 26 For a one-way ANOVA using α\alphaα = 0.05, the observed F value is ________.

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Probability

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Building Multiple Regression Models

Time-Series Forecasting and Index Numbers

Analysis of Categorical Data

Nonparametric Statistics

Statistical Quality Control

Decision Analysis

Filters

Data from a completely randomized design are shown in the following table. Treatment Level 1 2 3 27 26 27 26 22 29 23 21 27 24 23 26 For a one-way ANOVA using $\alpha$ = 0.05, the critical F value is ________.

Data from a randomized block design are shown in the following table. Treatment Levels Block 1 Block 2 Block3 1 8 6 7 2 5 6 8 3 10 9 8 4 7 5 9 With $\alpha$ = 0.05, the observed F value for the blocking effects null hypothesis is__.

For the following ANOVA table, the critical value of the studentized range distribution using $\alpha$ = 0.01 is ______. Source of Variation SS df MS F Treatrnent 0.1233 2 0.06165 1.566311 Error 0.5904 15 0.03936 Total 0.7137 17

Data from a completely randomized design are shown in the following table. Treatment Level 1 2 3 27 26 27 26 22 29 23 21 27 24 23 26 For a one-way ANOVA using $\alpha$ = 0.05, the observed F value is ________.