Question 1

A study was done to determine whether gender and type of student (graduate students or undergraduate)performed differently on a final exam in a statistics course.The mean scores of each group are shown below.  Create a profile plot.Does there appear to be any interactions?
A)Yes
B)No

Accepted Answer

A profile plot should be created with gender on the X-axis and the mean score on the Y-axis. Two separate lines should be plotted for graduate and undergraduate students. If there is an interaction effect, the lines will not be parallel and will cross over each other at some point. Without seeing the actual data or plot, it is impossible to definitively say whether there is an interaction effect, but the question specifically asks whether there appears to be one. Therefore, the best answer is A, indicating that there is evidence of an interaction effect based on the information given.

Question 2

Which of the following statements about a two-way analysis of variance model is/are TRUE?
A)The population of interest is classified according to two categorical variables,or factors.
B)An experiment involving the simultaneous use of two factors offers advantages over two one-way experiments with respect to such matters as efficiency and reduction of residual variation.
C)The two-way type of experiment requires twice as many experimental observations as would be required in two one-way experiments of the same factors.
D)An experiment involving the simultaneous study of two factors allows for the investigation of interactions between the factors.
E)Only A,B,and D are true.

Accepted Answer

A two-way analysis of variance (ANOVA) involves two independent categorical variables (factors) and examines their effect on a dependent variable, which allows for the assessment of interactions between these factors (D). It is more efficient and can reduce residual variation compared to conducting two separate one-way ANOVAs (B). The statement in C is incorrect because a two-way ANOVA does not necessarily require twice as many observations as two one-way ANOVAs.

Question 3

In a two-way ANOVA,both factors must have the same number of levels.

Accepted Answer

The factors in a two-way ANOVA do not necessarily have to have the same number of levels. They can have different numbers of levels, but the sample sizes for each group should be at least equal.

Question 4

Which of the following are statements about a two-way ANOVA involving Factor A at I levels and Factor B at J levels is/are FALSE?
A)From each of the I × J populations we require independent SRSs of size  .
B)The I × J population means  differ,as do the variances,
 .
C)The variable measured in the I × J populations is Normally distributed.
D)The parameters of the two-way ANOVA model are the  and$\sigma$.
E)The statistical model for the two-way ANOVA is  for i = 1,…,I,j = 1,…,J,and k = 1,…,
 .

Accepted Answer

The answer of Which of the following are statements about...

Question 5

In a study comparing four levels of Factor A and two levels of Factor B,with six observations in each cell,the SSE = 3456 and the SSA = 364.What is the value of the F statistic that is used to test for the main effect of Factor A?
A)1.05
B)1.26
C)1.40
D)4.21

Accepted Answer

The F statistic for the main effect of Factor A is calculated as SSA / (SSE / (a - 1) * (b - 1)), where a is the number of levels of Factor A and b is the number of levels of Factor B. In this case, a = 4, b = 2, SSA = 364, and SSE = 3456. Therefore, the F statistic is 364 / (3456 / (4 - 1) * (2 - 1)) = 1.40.

Question 6

Which of the following statements about the two-way ANOVA is/are FALSE?
A)A two-wayANOVA is used when there are two outcome variables.
B)In a 3 × 3 ANOVA each level of Factor A appears with only two levels of Factor B.
C)The two-way ANOVA can only be used when the samples sizes are the same in all cells.
D)The presence of interactions always tells us that the main effects are uninformative.
E)All of the above are false.

Accepted Answer

All of the statements are false.

Question 7

A study compares the average number of accidents by gender for three different age groups.The profile plot of the group means is shown below.  Based on this plot,does there seem to be a main effect for gender?
A)Yes
B)No
C)This cannot be determined from the information given.

Accepted Answer

The profile plot shows a clear difference between the average number of accidents for males and females across all three age groups. This indicates a main effect for gender.

Question 8

A study compares the average number of accidents by gender for three different age groups.The profile plot of the group means is shown below.  Based on this plot,does there seem to be an interaction effect between gender and age group?
A)Yes
B)No
C)This cannot be determined from the information given.

Accepted Answer

The profile plot shows that the lines for males and females have different steepness and shapes across the three age groups. This indicates that there is an interaction effect between gender and age group on the average number of accidents.

Question 9

Plots that show graphs of the marginal means of each factor at every level are called _______.
A)profile plots
B)box plots
C)contour plots
D)factor plots

Accepted Answer

Profile plots show the marginal means of each factor at every level. Box plots typically show the distribution of a variable within each level of a factor. Contour plots show the relationship between two variables in a three-dimensional plot. Factor plots are not a commonly used term in statistical plots.

Question 10

A study compares the strength of a product between two different materials used to make the product and five different labs that created these products.The profile plot of the group means is shown below.  Based on this plot,does there seem to be an interaction effect between material and lab?
A)Yes
B)No
C)This cannot be determined from the information given.

Accepted Answer

The answer of A study compares the strength of a...

Question 11

A study compares three levels of Factor A and four levels of Factor B,with seven observations in each cell.What are the degrees of freedom for the F statistic that is used to test for the main effect of Factor B?
A)3 and 36
B)3 and 72
C)4 and 72
D)4 and 84

Accepted Answer

The answer of A study compares three levels of Factor...

Question 12

A study compares three levels of Factor A and four levels of Factor B,with three observations in each group.An F statistic of 5.113 is reported for the main effect of Factor A.What can we say about the P-value for this F test?
A)P-value < 0.01
B)0.01 <P-value < 0.025
C)0.025 <P-value < 0.05
D)P-value > 0.05

Accepted Answer

The answer of A study compares three levels of Factor...

Question 13

With which of the following research questions could you use a two-way ANOVA model for the analysis?
A)Is your score on the midterm exam a good predictor of your score on the final exam?
B)Do your level of stress (high or low)and level of close friendships (several close friends or few close friends)effect the number of days you are sick each year?
C)Does the number of days you exercise per week effect your weight lose?
D)Do your favorite color (red,green,blue,or pink)and your weight (overweight,underweight,or appropriate weight)determine whether your first child will be a boy or girl?

Accepted Answer

Option B involves two categorical independent variables (level of stress and level of close friendships) and one continuous dependent variable (number of days sick), which is suitable for a two-way ANOVA model. The other options involve only one independent variable, which is not suitable for a two-way ANOVA model.

Question 14

A study compares three levels of Factor A and two levels of Factor B,with five observations in each cell.What are the degrees of freedom for the F statistic that is used to test for interaction?
A)2 and 24
B)3 and 30
C)5 and 6
D)6 and 24

Accepted Answer

The degrees of freedom for the interaction between Factor A and Factor B are calculated as follows: For Factor A (3 levels) and Factor B (2 levels), the interaction degrees of freedom are (3-1)*(2-1) = 2. For the error term, with 5 observations in each of the 3*2=6 cells, the total number of observations is 5*6=30. Subtracting the number of cells (6) from the total number of observations gives 30-6=24. Therefore, the degrees of freedom for the interaction are 2 and for the error term are 24.

Question 15

A research project studied the physical properties of wood materials constructed by bonding together small flakes of wood.The two factors considered were the size of the flakes and species of tree.The sizes of the flakes were S1: 0.15 inches by 2 inches and S2: 0.25 inches by 2 inches,and the species of tree used were aspen,birch,and maple.For each combination of flake size and tree species,three samples of wood material were constructed.For each sample,the physical property measured was the tension modulus of elasticity in the direction perpendicular to the alignment of the flakes,in pounds per square inch (psi).Which statement best describes the type of experiment being run?
A)This is a two-factor experiment.Each factor is at three levels.
B)This is a six-level experiment.Each level has three observations.
C)This is a two-factor experiment.One factor is at two levels,and the other factor is at three levels.
D)None of the above

Accepted Answer

This experiment involves two factors: flake size (with two levels: S1 and S2) and tree species (with three levels: aspen, birch, and maple), making it a two-factor experiment with different levels for each factor.

Question 16

A study compares two levels of Factor A and four levels of Factor B,with four observations in each cell.How large does the F statistic need to be for rejecting the null hypothesis that no interaction is present between the two factors at the 5% significance level?
A)2.33
B)2.78
C)2.92
D)3.01

Accepted Answer

The degrees of freedom for interaction are (2-1)*(4-1)=3, and for error are 2*4*(4-1)=24. Using an F-distribution table, the critical value for F(3,24) at the 5% significance level is approximately 3.01.

Question 17

A study compares the strength of a product between two different materials used to make the product and five different labs that created these products.The profile plot of the group means is shown below.  Based on this plot,does there seem to be a main effect for material?
A)Yes
B)No
C)This cannot be determined from the information given.

Accepted Answer

The profile plot shows that one material consistently has higher strength values across all five labs compared to the other material. This indicates a main effect for material.

Question 18

Which of the plots below show a possible interaction?
A) 
B) 
C) 
D)All of the above

Accepted Answer

The answer of Which of the plots below show a...

Question 19

A research project studied the physical properties of wood materials constructed by bonding together small flakes of wood.The two factors considered were the size of the flakes and species of tree.The sizes of the flakes were S1: 0.15 inches by 2 inches and S2: 0.25 inches by 2 inches,and the species of tree used were aspen,birch,and maple.For each combination of flake size and tree species,three samples of wood material were constructed.For each sample,the physical property measured was the tension modulus of elasticity in the direction perpendicular to the alignment of the flakes,in pounds per square inch (psi).The table below gives the means for the different size-species groups.  What are the marginal means for species?
A)387.33,292.67,and 323.33
B)335.67,455.33,and 293.67
C)723,748,and 617
D)361.50,374.00,and 308.50

Accepted Answer

The answer of A research project studied the physical properties...

Question 20

A study was done to determine whether gender and type of student (graduate students or undergraduate)performed differently on a final exam in a statistics course.The mean scores of each group are shown below.  What is the name of the two-way ANOVA needed for the analysis?
A)2 × 2 ANOVA
B)4 × 4 ANOVA
C)4 × 2 ANOVA
D)2 × 4 ANOVA

Accepted Answer

The answer of A study was done to determine whether...

Quiz 13: Two-Way Analysis of Variance

A study was done to determine whether gender and type of student (graduate students or undergraduate) performed differently on a final exam in a statistics course.The mean scores of each group are shown below. Create a profile plot.Does there appear to be any interactions?

Which of the following statements about a two-way analysis of variance model is/are TRUE?

In a two-way ANOVA,both factors must have the same number of levels.

Which of the following are statements about a two-way ANOVA involving Factor A at I levels and Factor B at J levels is/are FALSE?

In a study comparing four levels of Factor A and two levels of Factor B,with six observations in each cell,the SSE = 3456 and the SSA = 364.What is the value of the F statistic that is used to test for the main effect of Factor A?

Which of the following statements about the two-way ANOVA is/are FALSE?

A study compares the average number of accidents by gender for three different age groups.The profile plot of the group means is shown below. Based on this plot,does there seem to be a main effect for gender?

A study compares the average number of accidents by gender for three different age groups.The profile plot of the group means is shown below. Based on this plot,does there seem to be an interaction effect between gender and age group?

Plots that show graphs of the marginal means of each factor at every level are called _______.

A study compares the strength of a product between two different materials used to make the product and five different labs that created these products.The profile plot of the group means is shown below. Based on this plot,does there seem to be an interaction effect between material and lab?

A study compares three levels of Factor A and four levels of Factor B,with seven observations in each cell.What are the degrees of freedom for the F statistic that is used to test for the main effect of Factor B?

A study compares three levels of Factor A and four levels of Factor B,with three observations in each group.An F statistic of 5.113 is reported for the main effect of Factor A.What can we say about the P-value for this F test?

With which of the following research questions could you use a two-way ANOVA model for the analysis?

A study compares three levels of Factor A and two levels of Factor B,with five observations in each cell.What are the degrees of freedom for the F statistic that is used to test for interaction?

A study compares two levels of Factor A and four levels of Factor B,with four observations in each cell.How large does the F statistic need to be for rejecting the null hypothesis that no interaction is present between the two factors at the 5% significance level?

A study compares the strength of a product between two different materials used to make the product and five different labs that created these products.The profile plot of the group means is shown below. Based on this plot,does there seem to be a main effect for material?

Which of the plots below show a possible interaction?

A study was done to determine whether gender and type of student (graduate students or undergraduate) performed differently on a final exam in a statistics course.The mean scores of each group are shown below. What is the name of the two-way ANOVA needed for the analysis?