Question 1

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

Accepted Answer

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 
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 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

3
SSBL = 3[(2 - 2.5)

Question 4

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.

Accepted Answer

A) True 
 B)False

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 second group mean.

Accepted Answer

The answer of Consider the following calculations for a one-way...

Question 6

We reject H0: there is no difference between the four group means at a =.05.Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the groups and interpret the result.

Accepted Answer

See solution.
The margin of error for al

Question 7

$$\begin{array} { l l l l l l } 
\text { Block } & 1 & 2 & 3 & 4 & 5 \
\text { Tr1 } & 2 & 1 & 2 & 3 & 2 \
\text { Tr2 } & 4 & 4 & 1 & 1 & 2.5 \
\text { TR3 } & 3 & 4 & 3 & 2 & 3 \
\text { Mean } & 2 & 3 & 3 & 2 & \text { overall mean } = 2.5
\end{array}$$
Consider the randomized block design with 4 blocks and 3 treatments (groups) given above
-What is the between-groups (or treatment)sum of squares?

Accepted Answer

2 SSB = 4[(2 - 2.5)²

Question 8

In a two-way ANOVA,we must test for ________ between factor 1 and factor 2 prior to testing the significance of the main effects.

Accepted Answer

The answer of In a two-way ANOVA,we must test for...

Question 9

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

Accepted Answer

completely

Question 10

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

Accepted Answer

The answer of In performing a one-way ANOVA for a...

Question 11

$$\begin{array} { l c c c c } 
\text { Source } & \text { SS } & \text { DF } & \text { MS } & \text { F } \
\text { Factor A } & 2.25 & & .75 & \
\text { Factor B } & .95 & & .95 & \
\text { Interaction } & .90 & 3 & & \
\text { Error } & & & .15 & \
\text { Total } & 6.5 & 23 &
\end{array}$$
-Given the partial ANOVA table above,the calculated value of the F statistic for the interaction term is ____.

Accepted Answer

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

Question 12

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

Accepted Answer

1 SSB = 4[(2 - 2.5)²

Question 13

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.

Accepted Answer

A) True 
 B)False

Question 14

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?

Accepted Answer

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

Question 15

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

Accepted Answer

The answer of _____ simultaneous confidence intervals test all of...

Question 16

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
-Determine degrees of freedom treatment,degrees of freedom error and degrees of freedom total and state the critical value of the F statistic at a = .05.

Accepted Answer

d.f.(treatment)= 4,d

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

Is there a significant difference in the average fill amounts of the four machines?

Accepted Answer

The answer of Is there a significant difference in the...

Question 19

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.

Accepted Answer

A) True 
 B)False

Question 20

$$\begin{array} { l c c c c } 
\text { Source } & \text { SS } & \text { DF } & \text { MS } & \text { F } \
\text { Factor A } & 2.25 & & .75 & \
\text { Factor B } & .95 & & .95 & \
\text { Interaction } & .90 & 3 & & \
\text { Error } & & & .15 & \
\text { Total } & 6.5 & 23 &
\end{array}$$
-Given the partial ANOVA table above,the calculated value of the F statistic for Factor A is ____.

Accepted Answer

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

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

Source d.f. Sum of Squares Model 3 213.88125 Error 20 11.208333 Total 23 225.0895 -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.

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 block sum of squares?

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.

We reject H₀: there is no difference between the four group means at a =.05.Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the groups and interpret the result.

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 between-groups (or treatment)sum of squares?

In a two-way ANOVA,we must test for ________ between factor 1 and factor 2 prior to testing the significance of the main effects.

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

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

Source SS DF MS F Factor A 2.25 .75 Factor B .95 .95 Interaction .90 3 Error .15 Total 6.5 23 -Given the partial ANOVA table above,the calculated value of the F statistic for the interaction term is ____.

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 between-groups mean square?

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.

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?

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

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

Is there a significant difference in the average fill amounts of the four machines?

Source SS DF MS F Factor A 2.25 .75 Factor B .95 .95 Interaction .90 3 Error .15 Total 6.5 23 -Given the partial ANOVA table above,the calculated value of the F statistic for Factor A is ____.

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

Source d.f. Sum of Squares Model 3 213.88125 Error 20 11.208333 Total 23 225.0895 -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.

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 block sum of squares?

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.

We reject H0: there is no difference between the four group means at a =.05.Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the groups and interpret the result.

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 between-groups (or treatment)sum of squares?

In a two-way ANOVA,we must test for ________ between factor 1 and factor 2 prior to testing the significance of the main effects.

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

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

Source SS DF MS F Factor A 2.25 .75 Factor B .95 .95 Interaction .90 3 Error .15 Total 6.5 23 -Given the partial ANOVA table above,the calculated value of the F statistic for the interaction term is ____.

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 between-groups mean square?

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.

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?

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

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

Is there a significant difference in the average fill amounts of the four machines?

Source SS DF MS F Factor A 2.25 .75 Factor B .95 .95 Interaction .90 3 Error .15 Total 6.5 23 -Given the partial ANOVA table above,the calculated value of the F statistic for Factor A is ____.

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 the four group means at a =.05.Compute the Tukey simultaneous 95% confidence interval for all possible pairs of the groups and interpret the result.