Deck 10: Experimental Design and Analysis of Variance

Question 1

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.

Answer 1

True

Question 2

After rejecting the null hypothesis of equal means between three treatment groups,a researcher computes Tukey simultaneous 95% confidence intervals for the difference between each pair of treatments.If all of the confidence intervals exclude the value zero,then at $\alpha$
= 0.05 we can conclude that there are significant differences between all pairs of treatment group means.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

In a two-factor factorial experiment,the interaction effect between two factors can only be measured if there are multiple observations in each cell (combination of levels of two factors).

Question 5

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.

Question 6

When using a randomized block design,each block is used exactly once to measure the effect of each and every treatment.

Question 7

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

Question 8

In a one-way ANOVA for a completely randomized design,all other things being held constant,as two sample treatment group means get closer further apart the probability of rejecting the null hypothesis increases.

Question 9

If the total sum of squares in a one-way analysis of variance is 25 and the between-groups sum of squares is 17,then the error sum of squares is?

A)64
B)42
C)17
D)18
E)8

Question 10

In a one-way ANOVA for a completely randomized design, $q _ { \alpha }$
is always less than $t _ { \alpha / 2 }$
.

Question 11

In one-way ANOVA,the denominator of the F statistic is an estimate of the constant population variance of the treatment groups.

Question 12

In a completely randomized design,different levels of the factor are called _____.

A)treatments
B)variables
C)responses
D)observations
E)dependents

Question 13

If a researcher cannot control the factor being studied,then the researcher is carrying out a designed experiment.

Question 14

In a one-way ANOVA for a completely randomized design,all other things being held constant,as the sample treatment group means get closer to each other the probability of rejecting the null hypothesis decreases.

Question 15

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?

A)6
B)8
C)2
D)12
E)15

Question 16

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 between-groups sum of squares?

A)5
B)2
C)4
D)8
E)15

Question 17

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.

Question 18

In one-way ANOVA,the numerator degrees of freedom equals the number of treatment groups.

Question 19

In a one-way ANOVA for a completely randomized design,all other things being held constant,as the between-treatment variation decreases,the probability of rejecting the null hypothesis increases.

Question 20

The error sum of squares measures the between-treatment variability.

Question 21

In a one-way ANOVA for a completely randomized design with 4 groups and 15 observations per each group,the between-groups degrees of freedom is:

A)3
B)56
C)59
D)14
E)4

Question 22

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 total degrees of freedom is:

A)21
B)16
C)59
D)40
E)12

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:

A)21
B)16
C)59
D)40
E)12

Question 24

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

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 25

One difference between a one-way ANOVA and a two-way ANOVA is that in a two-way ANOVA we first test for a(n)_________ effect.

A)interaction
B)main
C)blocking
D)treatment
E)side

Question 26

When computing Tukey simultaneous confidence intervals for all possible pairwise comparisons of the treatment group means,the experimentwise error rate will be

A)equal to $\alpha$ .
B)less than $\alpha$ .
C)greater than $\alpha$ .

Question 27

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 between-groups sum of squares from your first analysis will be ______ the between-groups sum of squares from your second analysis.

A)equal to
B)less than
C)greater than
D)Cannot be determined.

Question 28

$$\begin{array} { l c c } \text { Source } & \text { d.f. } & \text { Sum of Squares } \\\text { Model } & 3 & 213.88125 \\\text { Error } & 20 & 11.208333 \\\text { Total } & 23 & 225.0895\end{array}$$

-Consider the above one-way ANOVA table.What is the treatment mean square?

A)71.29375
B)5604
C)1.297
D)213.881
E)9.7

Question 29

When computing individual confidence intervals based on the t distribution for all possible pairwise comparisons of the treatment group means,the experimentwise error rate will be

A)equal to $\alpha$ .
B)less than $\alpha$ .
C)greater than $\alpha$ .

Question 30

$$\begin{array} { l c c } \text { Source } & \text { d.f. } & \text { Sum of Squares } \\\text { Model } & 3 & 213.88125 \\\text { Error } & 20 & 11.208333 \\\text { Total } & 23 & 225.0895\end{array}$$

-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.

A)equal to
B)less than
C)greater than
D)Cannot be determined.

Question 31

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 interaction degrees of freedom is:

A)21
B)16
C)59
D)40
E)12

Question 32

In a one-way ANOVA for a completely randomized design with 4 groups and 15 observations per each group,the error degrees of freedom is:

A)3
B)56
C)59
D)14
E)4

Question 33

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.

A)equal to
B)less than
C)greater than
D)Cannot be determined.

Question 34

$$\begin{array} { l c c } \text { Source } & \text { d.f. } & \text { Sum of Squares } \\\text { Model } & 3 & 213.88125 \\\text { Error } & 20 & 11.208333 \\\text { Total } & 23 & 225.0895\end{array}$$

-Consider the above one-way ANOVA table.If there are an equal number of observations in each group,then each group (treatment level)consists of ______ observations.

A)3
B)4
C)6
D)20
E)24

Question 35

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

A)3
B)4
C)20
D)19
E)12

Question 36

In a one-way ANOVA for a completely randomized design,all other things being held constant,as the sample treatment group means get closer to each other the probability of rejecting the null hypothesis

A)decreases.
B)increases.
C)stays the same.
D)Cannot be determined.

Question 37

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

A)3
B)4
C)20
D)19
E)12

Question 38

$$\begin{array} { l c c } \text { Source } & \text { d.f. } & \text { Sum of Squares } \\\text { Model } & 3 & 213.88125 \\\text { Error } & 20 & 11.208333 \\\text { Total } & 23 & 225.0895\end{array}$$

-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 SSE from your first analysis will be ______ the SSE from your second analysis.

A)equal to
B)less than
C)greater than
D)Cannot be determined.

Question 39

$$\begin{array} { l c c } \text { Source } & \text { d.f. } & \text { Sum of Squares } \\\text { Model } & 3 & 213.88125 \\\text { Error } & 20 & 11.208333 \\\text { Total } & 23 & 225.0895\end{array}$$

-Consider the above one-way ANOVA table.How many groups (treatment levels)are included in the study?

A)3
B)4
C)6
D)20
E)24

Question 40

$$\begin{array} { l c c } \text { Source } & \text { d.f. } & \text { Sum of Squares } \\\text { Model } & 3 & 213.88125 \\\text { Error } & 20 & 11.208333 \\\text { Total } & 23 & 225.0895\end{array}$$

-Consider the above one-way ANOVA table.What is the mean square error?

A)71.297
B)5604
C)1.297
D)213.8810
E)9.7

Question 41

$$\begin{array} { l c c c c } \text { Source } & \text { SS } & \text { DF } & \text { MS } & \text { F } \\\text { Factor A } & 2.25 & & .75 & \\\text { Factor B } & .95 & & .95 & \\\text { Interaction } & .90 & 3 & & \\\text { Error } & & & .15 & \\\text { Total } & 6.5 & 23 &\end{array}$$

-Given the partial ANOVA table above,the number of levels of factor A are ____ and the number of levels factor B are ___.

A)3,1
B)4,2
C)6,1
D)4,24
E)1,16

Question 42

The advantage of the randomized block design over the completely randomized design is that we are comparing the treatments by using ________ experimental units.

A)randomly selected
B)the same
C)different
D)representative
E)equally timed

Question 43

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 total sum of squares from your first analysis will be ______ the total sum of squares from your second analysis.

A)equal to
B)less than
C)greater than
D)Cannot be determined.

Question 44

In performing a two-way ANOVA for a two-factor factorial experiment,the error sum of squares,SSE,equals:

A)SST - SS(groups)- SS(int)
B)SST - SS(1)- SS(2)- SSE
C)SST - SS(int)- SS(1)- SS(2)
D)SST - SS(1)- SS(2)
E)SST - SS(int)

Question 45

$$\begin{array} { l c c c c } \text { Source } & \text { SS } & \text { DF } & \text { MS } & \text { F } \\\text { Factor A } & 2.25 & & .75 & \\\text { Factor B } & .95 & & .95 & \\\text { Interaction } & .90 & 3 & & \\\text { Error } & & & .15 & \\\text { Total } & 6.5 & 23 &\end{array}$$

-Given the partial ANOVA table above,the calculated value of the F statistic for the interaction term is ____.

A)6.333
B)2.0
C)5.0
D)3.0
E)2.5

Question 46

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 F(groups)test statistic from your first analysis will be ______ the F(groups)test statistic from your second analysis.

A)equal to
B)less than
C)greater than
D)Cannot be determined.

Question 47

In performing a two-way ANOVA for a two-factor factorial experiment,the interaction sum of squares,SS(int),equals:

A)SST - SS(groups)- SSE
B)SST - SS(1)- SS(2)- SSE
C)SST - SSE - SS (1)
D)SST - SS(1)- SS(2)
E)SST - SSE

Question 48

In performing a two-way ANOVA for a two-factor factorial experiment,the total sum of squares,SST equals:

A)SS(1)+ SS(2)+ SSE
B)SS(1)+ SS (2)+ SS (int)
C)SS (int)+ SSE
D)SSE - SS(1)- SS(2)- SS(int)
E)SS(1)+ SS(2)+ SS(int)+ SSE

Question 49

In performing an ANOVA for a randomized block design,the between-groups sum of squares equals:

A)SST - SSE - SS(int)
B)SST - SSBL - SSE
C)SST - SS(int)- SSBL
D)SST - SSBL
E)SST - SSE

Question 50

Suppose that you analyze data from a randomized block experimental design using ANOVA.At the 5% level of significance,you reject the null hypothesis of equal treatment group means.You find out later that the data was actually from a completely randomized experimental design and use the one-way ANOVA procedure to reanalyze the data.For the completely randomized design ANOVA,the null hypothesis of equal treatment group means will ______ be rejected.

A)always
B)sometimes
C)never

Question 51

When we compute simultaneous 100 (1 - $\alpha$
)% confidence intervals,the value of a is called the

A)comparisonwise error rate.
B)Tukey simultaneous error rate.
C)experimentwise error rate.
D)pairwise error rate.
E)Type II error rate.

Question 52

A sum of squares that measures the variability among the group sample means is referred to as the _______ sum of squares.

A)between-groups
B)error
C)interaction
D)total
E)block

Question 53

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.

A)always
B)sometimes
C)never

Question 54

In performing a one-way ANOVA for a completely randomized design,the between-groups sum of squares equals:

A)SST - SSE - SS(int)
B)SST - SS(1)- SSE
C)SST - SS(int)- SS (1)- SS(2)
D)SST - SS(1)- SS(2)
E)SST - SSE

Question 55

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

A)The p populations of values of the response variable associated with the IV groups have equal variances.
B)The samples of experimental units associated with the groups are randomly selected.
C)The samples of experimental units associated with the groups are independent.
D)The number of sampled observations must be equal for all p treatments.
E)The p populations of values of the response variable within each group all have normal distributions.

Question 56

Suppose that you analyze data from a completely randomized experimental design using a one-way ANOVA.At the 5% level of significance,you reject the null hypothesis of equal treatment group means.You find out later that the data was actually from a randomized block experimental design and use the ANOVA procedure to reanalyze the data.For the randomized block design ANOVA,the null hypothesis of equal treatment group means will ______ be rejected at the 5% level of significance.

A)always
B)sometimes
C)never

Question 57

In performing a two-way ANOVA for a two-factor factorial experiment under which of the following circumstances would we test the significance of the main effects?

A)Substantial interaction exists between factors 1 and 2.
B)Little or no interaction exists between factors 1 and 2.
C)The factor 1 sum of squares equals the factor 2 sum of squares.
D)We reject the null hypothesis of no interaction.
E)The error sum of squares is equal to the interaction sum of squares.

Question 58

In performing a two-way ANOVA for a two-factor factorial experiment,we first test the _________.

A)significance of factor 1.
B)significance of factor 2.
C)significance of main effects.
D)interaction between factors 1 and 2.
E)significance of the error term.

Question 59

$$\begin{array} { l c c c c } \text { Source } & \text { SS } & \text { DF } & \text { MS } & \text { F } \\\text { Factor A } & 2.25 & & .75 & \\\text { Factor B } & .95 & & .95 & \\\text { Interaction } & .90 & 3 & & \\\text { Error } & & & .15 & \\\text { Total } & 6.5 & 23 &\end{array}$$

-Given the partial ANOVA table above,the calculated value of the F statistic for Factor A is ____.

A)6.333
B)2.0
C)5.0
D)3.0
E)2.5

Question 60

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.

A)between-groups
B)error
C)interaction
D)total
E)block

Question 61

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?

A)20
B)4
C)3
D)19
E)16

Question 62

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 treatments?

A)20
B)4
C)3
D)19
E)16

Question 63

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 total?

A)20
B)4
C)3
D)19
E)16

Question 64

In one-way ANOVA for a completely randomized design,the total sum of squares is equal to _______________________.

Question 65

In performing a one-way ANOVA for a completely randomized design,the _________ mean square measures the variability of the group means.

Question 66

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.

Question 67

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 factor 1,the numerator and denominator degrees of freedom for the ANOVA F test are:

A)4,60
B)3,48
C)4,48
D)3,12
E)4,12

Question 68

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.

Question 69

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

Question 70

_____ refers to applying an IV to more than one experimental unit.

Question 71

_____ simultaneous confidence intervals test all of the pairwise differences between means respectively while controlling the overall Type I error.

Question 72

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

Question 73

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

Question 74

In a ___________________ experimental design,independent random samples of experimental units are assigned to the groups.

Question 75

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,

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 76

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.

Question 77

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.

Question 78

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

A)biased
B)response
C)random
D)unknown
E)independent

Question 79

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:

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

Question 80

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:

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.