Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. \[\begin{array} { c c c c } & & { \text { Factor I } } \\ \text { Factor II } & 1 & 2 & 3 \\ 1 & 4 & 8 & 5 \\ & 6 & 7 & 5 \\ & 5 & 5 & 6 \\ & & & \\ 2 & 4 & 5 & 0 \\ & 2 & 3 & 1 \\ & 3 & 2 & 1 \end{array}\] -What is the degrees of freedom for factor I?

The answer of Consider the following data from a two-factor...

Consider the following data from a two-factor factorial experiment.You wish to perform a two-way analysis of variance to analyze the data. \[\begin{array} { c c c c } & & { \text { Factor I } } \\ \text { Factor II } & 1 & 2 & 3 \\ 1 & 4 & 8 & 5 \\ & 6 & 7 & 5 \\ & 5 & 5 & 6 \\ & & & \\ 2 & 4 & 5 & 0 \\ & 2 & 3 & 1 \\ & 3 & 2 & 1 \end{array}\] -What is the factor I mean square?

The answer of Consider the following data from a two-factor...

\[\begin{array} { l l l l l l } \text { Block } & 1 & 2 & 3 & 4 & 5 \\ \text { Tr1 } & 2 & 1 & 2 & 3 & 2 \\ \text { Tr2 } & 4 & 4 & 1 & 1 & 2.5 \\ \text { TR3 } & 3 & 4 & 3 & 2 & 3 \\ \text { Mean } & 2 & 3 & 3 & 2 & \text { overall mean } = 2.5 \end{array}\] Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the error mean square?

1.667 SST = (2 - 2.5) 2 + (1 - 2.5) 2 + (2 -

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 the blocks.

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. -Use the information above and determine an individual 95% confidence interval confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ )The mean and sample sizes for brand 1 and brand 2 are as follows: $\bar { x } _ { 1 }$ = 2)95, $\bar { x } _ { 2 }$ = 2)28,n1 = 4 and n2 = 5.

A) 2013 to 1.1387 B) 2852 to 1.0547 C) -.228 to 1.5680 D) 4515 to .8885 E) It cannot be determined with the information given. A) 2013 to 1.1387 B) 2852 to 1.0547 C) -.228 to 1.5680 D) 4515 to .8885 E) It cannot be determined with the information given.

Exam 10: Experimental Design and Analysis of Variance

In a one-way analysis of variance for a completely randomized design with three treatments groups,each with five measurements,what are the degrees of freedom associated with the error sum of squares?

(Multiple Choice)

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Question 21

We reject H₀: there is no difference between effects of levels of factor I at a =.05.Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the levels of factor I and interpret the result.You are given that MSE = 1.2222.

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Question 22

The 95% individual confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ will always be narrower than the Tukey 95% simultaneous confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

(True/False)

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Question 23

Consider a two-factor factorial experiment with 4 levels of factor 1,5 levels of factor 2,and 3 observations per cell.If we use a two-way ANOVA to analyze the data from this experiment,the error degrees of freedom is:

(Multiple Choice)

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Question 24

When computing a confidence interval for the difference between two means,the width of the 100(1 - $\alpha$ )% Tukey simultaneous confidence interval will be __________ the width of the 100(1 - $\alpha$ )% individual confidence interval based on the t distribution.

(Multiple Choice)

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Question 25

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 factor I?

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Question 26

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 factor I mean square?

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Question 27

The F-test for testing the difference between group means is equal to the ___ mean squares divided by the _ mean square.

(Short Answer)

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Question 28

Block 1 2 3 4 5 Tr1 2 1 2 3 2 Tr2 4 4 1 1 2.5 TR3 3 4 3 2 3 Mean 2 3 3 2 overall mean =2.5 Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the error mean square?

(Essay)

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Question 29

A machine manufacturer conducted a study to compare the performance of two types of similar machines A and B in terms of the hardness of the product manufactured.According to the production supervisor,the machine setting (high,medium,low)also affects the hardness of the product.The hardness readings (response variable)are given in a two-factor factorial design format with two observations per cell. Machine type Machine Setting A B Low 8 4 8 4 Medium 7 5 6 2 High 9 4 10 5 You are also given the following additional information: SS (machine type)= 48,SS (machine setting)= 8,SST = 64 -Determine SS(int)and SSE.

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Question 30

Find an individual 95 percent confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ where $\bar { x } _ { 1 }$ = 33.98, $\bar { x } _ { 2 }$ = 36.56,and MSE = 0.669.There were 15 observations in total and 3 treatments.Assume that the number of observations in each treatment is equal.

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Question 31

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 treatment mean square?

(Essay)

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Question 32

A researcher has used a one-way analysis of variance model to test whether the average starting salaries differ among the recent graduates from nursing, engineering, business and education disciplines. The researcher has randomly selected four graduates from each of the four areas. -If MSE = 4,and SST = 120 complete the following ANOVA table and determine the value of the F statistic.Note that "group" has been labeled as "treatment".

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Question 33

Test H₀: there is no difference between group (treatment)effects at a = .05.State the F value and make your decision.

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Question 34

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 the blocks.

(Essay)

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Question 35

Block 1 2 3 4 5 Tr1 2 1 2 3 2 Tr2 4 4 1 1 2.5 TR3 3 4 3 2 3 Mean 2 3 3 2 overall mean =2.5 Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the blocks mean square?

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Question 36

In general,a Tukey simultaneous 100(1 - $\alpha$ )percent confidence interval is _____ than the corresponding individual 100(1 - $\alpha$ )percent confidence interval.

(Short Answer)

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Question 37

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. -Use the information above and determine an individual 95% confidence interval confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ )The mean and sample sizes for brand 1 and brand 2 are as follows: $\bar { x } _ { 1 }$ = 2)95, $\bar { x } _ { 2 }$ = 2)28,n₁ = 4 and n₂ = 5.

(Multiple Choice)

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Question 38

The error degrees of freedom for a randomized block design ANOVA test with 4 treatment groups and 5 blocks is:

(Multiple Choice)

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Question 39

The dependent variable,the variable of interest in an experiment,is also called the ___________ variable.

(Short Answer)

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Question 40

In a one-way analysis of variance for a completely randomized design with three treatments groups,each with five measurements,what are the degrees of freedom associated with the error sum of squares?

We reject H₀: there is no difference between effects of levels of factor I at a =.05.Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the levels of factor I and interpret the result.You are given that MSE = 1.2222.

The 95% individual confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ will always be narrower than the Tukey 95% simultaneous confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

Consider a two-factor factorial experiment with 4 levels of factor 1,5 levels of factor 2,and 3 observations per cell.If we use a two-way ANOVA to analyze the data from this experiment,the error degrees of freedom is:

When computing a confidence interval for the difference between two means,the width of the 100(1 - $\alpha$ )% Tukey simultaneous confidence interval will be __________ the width of the 100(1 - $\alpha$ )% individual confidence interval based on the t distribution.

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 factor I?

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 factor I mean square?

The F-test for testing the difference between group means is equal to the ___ mean squares divided by the _ mean square.

Block 1 2 3 4 5 Tr1 2 1 2 3 2 Tr2 4 4 1 1 2.5 TR3 3 4 3 2 3 Mean 2 3 3 2 overall mean =2.5 Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the error mean square?

Find an individual 95 percent confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ where $\bar { x } _ { 1 }$ = 33.98, $\bar { x } _ { 2 }$ = 36.56,and MSE = 0.669.There were 15 observations in total and 3 treatments.Assume that the number of observations in each treatment is equal.

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 treatment mean square?

Test H₀: there is no difference between group (treatment)effects at a = .05.State the F value and make your decision.

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 the blocks.

Block 1 2 3 4 5 Tr1 2 1 2 3 2 Tr2 4 4 1 1 2.5 TR3 3 4 3 2 3 Mean 2 3 3 2 overall mean =2.5 Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the blocks mean square?

In general,a Tukey simultaneous 100(1 - $\alpha$ )percent confidence interval is _____ than the corresponding individual 100(1 - $\alpha$ )percent confidence interval.

The error degrees of freedom for a randomized block design ANOVA test with 4 treatment groups and 5 blocks is:

The dependent variable,the variable of interest in an experiment,is also called the ___________ 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

Exam 10: Experimental Design and Analysis of Variance

In a one-way analysis of variance for a completely randomized design with three treatments groups,each with five measurements,what are the degrees of freedom associated with the error sum of squares?

We reject H0: there is no difference between effects of levels of factor I at a =.05.Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the levels of factor I and interpret the result.You are given that MSE = 1.2222.

The 95% individual confidence interval for μ1−μ2\mu _ { 1 } - \mu _ { 2 }μ1​−μ2​ will always be narrower than the Tukey 95% simultaneous confidence interval for μ1−μ2\mu _ { 1 } - \mu _ { 2 }μ1​−μ2​ .

Consider a two-factor factorial experiment with 4 levels of factor 1,5 levels of factor 2,and 3 observations per cell.If we use a two-way ANOVA to analyze the data from this experiment,the error degrees of freedom is:

When computing a confidence interval for the difference between two means,the width of the 100(1 - α\alphaα )% Tukey simultaneous confidence interval will be __________ the width of the 100(1 - α\alphaα )% individual confidence interval based on the t distribution.

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 factor I?

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 factor I mean square?

The F-test for testing the difference between group means is equal to the _____________ mean squares divided by the ___________ mean square.

Block 1 2 3 4 5 Tr1 2 1 2 3 2 Tr2 4 4 1 1 2.5 TR3 3 4 3 2 3 Mean 2 3 3 2 overall mean =2.5 Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the error mean square?

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 treatment mean square?

Test H0: there is no difference between group (treatment)effects at a = .05.State the F value and make your decision.

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 the blocks.

Block 1 2 3 4 5 Tr1 2 1 2 3 2 Tr2 4 4 1 1 2.5 TR3 3 4 3 2 3 Mean 2 3 3 2 overall mean =2.5 Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the blocks mean square?

In general,a Tukey simultaneous 100(1 - α\alphaα )percent confidence interval is _____ than the corresponding individual 100(1 - α\alphaα )percent confidence interval.

The error degrees of freedom for a randomized block design ANOVA test with 4 treatment groups and 5 blocks is:

The dependent variable,the variable of interest in an experiment,is also called the ___________ 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

We reject H₀: there is no difference between effects of levels of factor I at a =.05.Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the levels of factor I and interpret the result.You are given that MSE = 1.2222.

The 95% individual confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ will always be narrower than the Tukey 95% simultaneous confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ .

When computing a confidence interval for the difference between two means,the width of the 100(1 - $\alpha$ )% Tukey simultaneous confidence interval will be __________ the width of the 100(1 - $\alpha$ )% individual confidence interval based on the t distribution.

The F-test for testing the difference between group means is equal to the ___ mean squares divided by the _ mean square.

Test H₀: there is no difference between group (treatment)effects at a = .05.State the F value and make your decision.

In general,a Tukey simultaneous 100(1 - $\alpha$ )percent confidence interval is _____ than the corresponding individual 100(1 - $\alpha$ )percent confidence interval.