Question 1

At the 5% level of significance,is there a difference in the average starting salaries among the four disciplines?

Accepted Answer

Reject H₀,The average starting

Question 2

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 with the remaining factor using the same data,the SSE will always be larger than 5.5.

Accepted Answer

A) True 
 B)False

Question 3

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.

-At a significance level of 0.05,the null hypothesis for the ANOVA F test is rejected.Analysis of the Tukey's simultaneous confidence intervals shows that at the significance level (experimentwise)of 0.05 we would conclude that,in regards to average time,

Accepted Answer

A) all four brands of vacuum cleaners differ from each other in terms of their performance. 
B) brand 1 differs from brand 2,and brand 2 differs from brand 3 while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance. 
C) brand 1 differs from brand 2,and brand 3 differs from brands 1,2 and 4,while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance. 
D) only brand 3 differs from the other three brands (brands 1,2 and 3),while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance. 
E) none of the four brands of vacuum cleaners differ from each other in terms of their performance. 
A) all four brands of vacuum cleaners differ from each other in terms of their performance. 
B) brand 1 differs from brand 2,and brand 2 differs from brand 3 while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance. 
C) brand 1 differs from brand 2,and brand 3 differs from brands 1,2 and 4,while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance. 
D) only brand 3 differs from the other three brands (brands 1,2 and 3),while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance. 
E) none of the four brands of vacuum cleaners differ from each other in terms of their performance.

Question 4

A two-way ANOVA for a two-factor factorial design has 4 levels of factor 1, 3 levels of factor 2, and 5 observations per cell.
-In testing the significance of interaction,the numerator and denominator degrees of freedom for the ANOVA F test are:

Accepted Answer

A) 5,12 
B) 5,60 
C) 5,48 
D) 6,48 
E) 12,48 
A) 5,12 
B) 5,60 
C) 5,48 
D) 6,48 
E) 12,48

Question 5

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 block mean square?

Accepted Answer

[42.09/(6

Question 6

A _____ design,is an experimental design that compares p groups by using b blocks,where each block is used exactly once to measure the effect of each treatment.

Accepted Answer

The answer of A _____ design,is an experimental design that...

Question 7

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.
-At a significance level of 0.05,we would:

Accepted Answer

A) Not be able to reject the null hypothesis of equal treatment group means. 
B) Reject the null hypothesis of equal treatment group means. 
C) Reject or fail to reject depending on the value of the t statistic. 
D) Not be able to decide whether or not to reject the null hypothesis due to insufficient information. 
E) Reject the significance level of the error term. 
A) Not be able to reject the null hypothesis of equal treatment group means. 
B) Reject the null hypothesis of equal treatment group means. 
C) Reject or fail to reject depending on the value of the t statistic. 
D) Not be able to decide whether or not to reject the null hypothesis due to insufficient information. 
E) Reject the significance level of the error term.

Question 8

When using a one -way ANOVA to analyze data from a completely randomized design,the calculated F statistic will decrease as _____.

Accepted Answer

A) the between-group variability decreases relative to the within-group variability 
B) the total variability increases 
C) the total variability decreases 
D) the between-group variability increases relative to the within-group variability 
E) Cannot be determined. 
A) the between-group variability decreases relative to the within-group variability 
B) the total variability increases 
C) the total variability decreases 
D) the between-group variability increases relative to the within-group variability 
E) Cannot be determined.

Question 9

A one-way analysis of variance is a method that allows us to estimate and compare the effects of several treatments on a response variable.

Accepted Answer

A) True 
 B)False

Question 10

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. $\begin{array}{cc}&\text { Machine type }\
\text { Machine Setting }&\text { A } & \text { B } \
\text { Low }&8 & 4 \
&8 & 4 \\
\text { Medium }&7 & 5 \
&6 & 2 \\
\text { High }&9 & 4 \
&10 & 5
\end{array}$ You are also given the following additional information:
SS (machine type)= 48,SS (machine setting)= 8,SST = 64
-Complete the analysis of variance table and test to determine whether the means for factor B differ at a = .10.Interpret the results.

Accepted Answer

Reject H₀ .There is a significant differe

Question 11

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 error.

Accepted Answer

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

Question 12

Is there a significant difference in the annual sales of the five company categories?

Accepted Answer

F = 7.5 > F_.05,4,50 = 2.57,therefore r

Question 13

Consider the following partial analysis of variance table from a randomized block design with 6 blocks and 4 groups (treatments). $$\begin{array} { l c } 
\text { Source } & \text { Sum of Squares } \
\text { Treatments } & 15.93 \
\text { Blocks } & 42.09 \
\text { Error } & 23.84 \
\text { Total } & 81.86
\end{array}$$
-Determine the degrees of freedom for groups (treatments).

Accepted Answer

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

Question 14

In one-way ANOVA,a large value of F results when the within-treatment variability is large compared to the between-treatment variability.

Accepted Answer

A) True 
 B)False

Question 15

A company that fills containers of water has four machines.The quality control manager needs to determine whether the average fill for these machines is the same.Looking at 19 containers,we have the following data of fill measures in litres: $$\begin{array} { l l l l l } 
& \text { Machine 1 } & \text { Machine 2 } & \text { Machine 3 } & \text { Machine 4 } \
\mathrm { N } & 4 & 6 & 5 & 4 \
\bar { x } & 4.03 & 4.0017 & 3.974 & 4.005 \
\mathrm {~S} & 0.0183 & 0.0117 & 0.0182 & 0.0129
\end{array}$$ and the following partial ANOVA table (with "group" labeled as "treatment"): $$\begin{array} { l c c c c } 
\text { Source } & \text { SS } & \text { d.f. } & \text { MS } & \text { F } \
\text { Treatments } & & & 0.002359 \
\text { Errors } & & & \
\text { Total } & 0.010579 & &
\end{array}$$
-Complete the ANOVA table and calculate F.

Accepted Answer

The answer of A company that fills containers of water...

At the 5% level of significance,is there a difference in the average starting salaries among the four disciplines?

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 with the remaining factor using the same data,the SSE will always be larger than 5.5.

A two-way ANOVA for a two-factor factorial design has 4 levels of factor 1, 3 levels of factor 2, and 5 observations per cell. -In testing the significance of interaction,the numerator and denominator degrees of freedom for the ANOVA F test are:

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 block mean square?

A _____ design,is an experimental design that compares p groups by using b blocks,where each block is used exactly once to measure the effect of each treatment.

When using a one -way ANOVA to analyze data from a completely randomized design,the calculated F statistic will decrease as _____.

A one-way analysis of variance is a method that allows us to estimate and compare the effects of several treatments on a response variable.

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 error.

Is there a significant difference in the annual sales of the five company categories?

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 -Determine the degrees of freedom for groups (treatments).

In one-way ANOVA,a large value of F results when the within-treatment variability is large compared to the between-treatment variability.

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

At the 5% level of significance,is there a difference in the average starting salaries among the four disciplines?

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 with the remaining factor using the same data,the SSE will always be larger than 5.5.

A two-way ANOVA for a two-factor factorial design has 4 levels of factor 1, 3 levels of factor 2, and 5 observations per cell. -In testing the significance of interaction,the numerator and denominator degrees of freedom for the ANOVA F test are:

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 block mean square?

A _____ design,is an experimental design that compares p groups by using b blocks,where each block is used exactly once to measure the effect of each treatment.

When using a one -way ANOVA to analyze data from a completely randomized design,the calculated F statistic will decrease as _____.

A one-way analysis of variance is a method that allows us to estimate and compare the effects of several treatments on a response variable.

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 error.

Is there a significant difference in the annual sales of the five company categories?

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 -Determine the degrees of freedom for groups (treatments).

In one-way ANOVA,a large value of F results when the within-treatment variability is large compared to the between-treatment variability.

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