Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 groups (treatments). \[\begin{array} { l c } \text { Source } & \text { SS } \\ \text { Treatments } & 2,477.53 \\ \text { Blocks } & 3,180.48 \\ \text { Error } & 11,661.38 \\ \text { Total } & \end{array}\] -Determine the degrees of freedom for groups (treatments).

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Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 groups (treatments). \[\begin{array} { l c } \text { Source } & \text { Sum of Squares } \\ \text { Treatments } & 15.93 \\ \text { Blocks } & 42.09 \\ \text { Error } & 23.84 \\ \text { Total } & 81.86 \end{array}\] -What is the calculated F statistic for groups (treatments)?

The answer of Consider the following partial analysis of variance...

ANOVA table $\begin{array}{lrrrr} \hline\text { Source } & S S & d f & M S & F &p \text {-value }\\ \hline \text { Treatment } & 6.000 & 3 & 1.9998 & 18.85&3.4E-05\\ \hline\text { Error } & 1.486 & 14 & 0.1061 & \\ \hline\text { Total } & 7.485 & 17 & & \end{array}$ Post hoc analysis Tukey simultaneous comparison t-values $ ( $ d.f. $ =14) $ $\begin{array}{ccccc} &\text { Brand 3 } \text { Brand 2 } \text { Brand 4 } \text { Brand 1 } \\ &\quad1.40 \quad 2.28 \quad 2.58 \quad 2.95\\ \begin{array}{ll} \text { Brand 3 } & 1.40 \\ \text { Brand 2 } & 2.28 \\ \text { Brand 4 } & 2.58 \\ \text { Brand 1 } & 2.95 \end{array}&\begin{array}{|l|l|l|l|} \hline & & & \\ \hline 4.27 & & & \\ \hline 5.38 & 1.35 & & \\ \hline 7.09 & 3.07 & 1.63 &\quad\quad \\ \hline \end{array} \end{array}$ The Excel/Mega-Stat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners. The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt. -What is the total number of observations for all brands of vacuum cleaners (total sample size)?

A) 14 B) 17 C) 18 D) 19 E) 20 A) 14 B) 17 C) 18 D) 19 E) 20

Exam 10: Experimental Design and Analysis of Variance

Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. Factor I Factor II 1 2 3 1 4 8 5 6 7 5 5 5 6 2 4 5 0 2 3 1 3 2 1 -What is the degrees of freedom for error?

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Question 1

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(3)(2)(3-1)= 12

Find the 95% confidence interval for treatment 2,factor 1.(MSE = 1.22)

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4.02 to 5.98 $\begin{array} { l } t _ { .025,12 } = 2.179 \\5 \pm ( 2.179 ) \sqrt { \frac { 1.22 } { 6 } } \rightarrow 4.02 \text { to } 5.98\end{array}$

Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. Factor I Factor II 1 2 3 1 4 8 5 6 7 5 5 5 6 2 4 5 0 2 3 1 3 2 1 -What is the mean square error?

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1.22 $S S ( \text { Total } ) = \left[ ( 4 - 4 ) ^ { 2 } + ( 8 - 4 ) ^ { 2 } + ( 5 - 4 ) ^ { 2 } + ( 6 - 4 ) ^ { 2 } + ( 7 - 4 ) ^ { 2 } + \ldots + ( 1 - 4 ) ^ { 2 } \right] = 82$
$\operatorname { SS } ( \text { Factor } 1 ) = 6 \left[ ( 4 - 4 ) ^ { 2 } + ( 5 - 4 ) ^ { 2 } + ( 3 - 4 ) ^ { 2 } \right] = 12$
$\operatorname { SS } ( \text { Factor } 2 ) = 9 \left[ ( 5.667 - 4 ) ^ { 2 } + ( 2.333 - 4 ) ^ { 2 } \right] = 50$
$\begin{array} { l } S S ( \text { Interaction } ) = 3 \left[ ( 5 - 5.667 - 4 + 4 ) ^ { 2 } + ( 6.667 - 5.667 - 5 + 4 ) ^ { 2 } \ldots + ( 0.667 - 2.333 - 3 + 4 ) ^ { 2 } \right] \\S S ( \text { Interaction } ) = 3 ( 1.778 ) = 5.333\end{array}$
SSE = 82 -12 -50 - 5.333 = 14.667 $M S E = \frac { 14.667 } { ( 2 ) ( 3 ) ( 3 - 1 ) } = 1.22$

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 4 groups and 5 observations per group.The response variable is sales in millions of dollars and four groups represent the four regions that the company serves. MSE = 101.25, $\bar { x } _ { 1 }$ = 33, $\bar { x } _ { 2 }$ = 43, $\bar { x } _ { 3 }$ = 49, $\bar { x } _ { 4 }$ = 28 -Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the 4 groups and interpret the result within the context of the question.

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Question 4

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 groups (treatments). Source SS Treatments 2,477.53 Blocks 3,180.48 Error 11,661.38 Total -Determine the degrees of freedom for groups (treatments).

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Question 5

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 4 groups and 5 observations per group.The response variable is sales in millions of dollars and four groups represent the four regions that the company serves. MSE = 101.25, $\bar { x } _ { 1 }$ = 33, $\bar { x } _ { 2 }$ = 43, $\bar { x } _ { 3 }$ = 49, $\bar { x } _ { 4 }$ = 28 -Compute an individual 95% confidence interval for the first group mean.

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Question 6

Looking at four different diets, a researcher randomly assigned 20 equally overweight adults into each of the four diets. The researcher wishes to use a one-way ANOVA to analyze the data. -What is the degrees of freedom for the error?

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Question 7

Consider a two-factor factorial experiment with 3 levels of factor 1,5 levels of factor 2,and 3 observations in each cell.If you wish to perform a two-way ANOVA on the resulting data,determine the degrees of freedom for factor 1,degrees of freedom for factor 2,degrees of freedom interaction,degrees of freedom error,and degrees of freedom total.

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Question 8

The ______________ units are the entities (objects,people,etc. )to which the different IV levels are assigned.

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Question 9

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 groups (treatments). Source Sum of Squares Treatments 15.93 Blocks 42.09 Error 23.84 Total 81.86 -What is the calculated F statistic for groups (treatments)?

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Question 10

Source d.f. Sum of Squares Model 3 213.88125 Error 20 11.208333 Total 23 225.0895 -Suppose that you analyze data from a completely randomized experimental design using a one-way ANOVA.You find out later that the data was actually from a randomized block experimental design and use the ANOVA procedure to reanalyze the data.The MSE from your first analysis will be ______ the MSE from your second analysis.

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Question 11

Consider the following calculations for a one-way analysis of variance from a completely randomized design with 4 groups and 5 observations per group.The response variable is sales in millions of dollars and four groups represent the four regions that the company serves. MSE = 101.25, $\bar { x } _ { 1 }$ = 33, $\bar { x } _ { 2 }$ = 43, $\bar { x } _ { 3 }$ = 49, $\bar { x } _ { 4 }$ = 28 -Compute an individual 95% confidence interval for $\mu _ { 3 } - \mu _ { 4 }$ .

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Question 12

In performing a one-way ANOVA,the _________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response,and its corresponding group mean.

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Question 13

ANOVA table Source SS df MS F p -value Treatment 6.000 3 1.9998 18.85 3.4E-05 Error 1.486 14 0.1061 Total 7.485 17 Post hoc analysis Tukey simultaneous comparison t-values $($ d.f. $=14)$ Brand 3 nbsp; Brand 2 nbsp; Brand 4 nbsp; Brand 1 1.402.282.582.95 Brand 3 1.40 Brand 2 2.28 Brand 4 2.58 Brand 1 2.95 4.27 5.38 1.35 7.09 3.07 1.63 The Excel/Mega-Stat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners. The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt. -What is the total number of observations for all brands of vacuum cleaners (total sample size)?

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Question 14

Based on the results of a two-factor factorial experiment,the ANOVA table showed that SSE = 5.5.If we ignore one of the factors and perform a one-way ANOVA using the same data,the SSE will _________________ be smaller than 5.5.

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Question 15

Which of the following is not an assumption required for a one-way analysis of variance?

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Question 16

A test is conducted to compare four different brands of batteries to determine if there is any difference in the average life,in hours,they provide under laboratory conditions.Ten different electronic devices are selected and each device uses all three brands of batteries in a random order.The number of hours is recorded for each battery used.This is an example of a(n)_________ experimental design.

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Question 17

The sum of squares that measures the total amount of variability in the observed values of the response variable is referred to as the _______ sum of squares.

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Question 18

Test H₀: there is no difference between the block effects at $\alpha$ = .05.

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Question 19

Suppose that a teacher wants to study how four different study methods affect a student's final grade.The study method is the dependent variable.

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Question 20

Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. Factor I Factor II 1 2 3 1 4 8 5 6 7 5 5 5 6 2 4 5 0 2 3 1 3 2 1 -What is the degrees of freedom for error?

Find the 95% confidence interval for treatment 2,factor 1.(MSE = 1.22)

Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. Factor I Factor II 1 2 3 1 4 8 5 6 7 5 5 5 6 2 4 5 0 2 3 1 3 2 1 -What is the mean square error?

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 groups (treatments). Source SS Treatments 2,477.53 Blocks 3,180.48 Error 11,661.38 Total -Determine the degrees of freedom for groups (treatments).

Looking at four different diets, a researcher randomly assigned 20 equally overweight adults into each of the four diets. The researcher wishes to use a one-way ANOVA to analyze the data. -What is the degrees of freedom for the error?

The ______________ units are the entities (objects,people,etc. )to which the different IV levels are assigned.

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 groups (treatments). Source Sum of Squares Treatments 15.93 Blocks 42.09 Error 23.84 Total 81.86 -What is the calculated F statistic for groups (treatments)?

In performing a one-way ANOVA,the _________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response,and its corresponding group mean.

Based on the results of a two-factor factorial experiment,the ANOVA table showed that SSE = 5.5.If we ignore one of the factors and perform a one-way ANOVA using the same data,the SSE will _________________ be smaller than 5.5.

Which of the following is not an assumption required for a one-way analysis of variance?

The sum of squares that measures the total amount of variability in the observed values of the response variable is referred to as the _______ sum of squares.

Test H₀: there is no difference between the block effects at $\alpha$ = .05.

Suppose that a teacher wants to study how four different study methods affect a student's final grade.The study method is the dependent variable.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

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Exam 10: Experimental Design and Analysis of Variance

Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. Factor I Factor II 1 2 3 1 4 8 5 6 7 5 5 5 6 2 4 5 0 2 3 1 3 2 1 -What is the degrees of freedom for error?

Find the 95% confidence interval for treatment 2,factor 1.(MSE = 1.22)

Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. Factor I Factor II 1 2 3 1 4 8 5 6 7 5 5 5 6 2 4 5 0 2 3 1 3 2 1 -What is the mean square error?

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 groups (treatments). Source SS Treatments 2,477.53 Blocks 3,180.48 Error 11,661.38 Total -Determine the degrees of freedom for groups (treatments).

Looking at four different diets, a researcher randomly assigned 20 equally overweight adults into each of the four diets. The researcher wishes to use a one-way ANOVA to analyze the data. -What is the degrees of freedom for the error?

The ______________ units are the entities (objects,people,etc. )to which the different IV levels are assigned.

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 groups (treatments). Source Sum of Squares Treatments 15.93 Blocks 42.09 Error 23.84 Total 81.86 -What is the calculated F statistic for groups (treatments)?

In performing a one-way ANOVA,the _________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response,and its corresponding group mean.

Based on the results of a two-factor factorial experiment,the ANOVA table showed that SSE = 5.5.If we ignore one of the factors and perform a one-way ANOVA using the same data,the SSE will _________________ be smaller than 5.5.

Which of the following is not an assumption required for a one-way analysis of variance?

The sum of squares that measures the total amount of variability in the observed values of the response variable is referred to as the _______ sum of squares.

Test H0: there is no difference between the block effects at α\alphaα = .05.

Suppose that a teacher wants to study how four different study methods affect a student's final grade.The study method is the dependent variable.

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Correlation Coefficient and Simple Linear Regression Analysis

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

Test H₀: there is no difference between the block effects at $\alpha$ = .05.