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

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

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

The answer of \[\begin{array} { l l l l l...

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

The answer of We reject H₀: there is no difference...

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

The answer of \[\begin{array} { l l l l l...

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

The answer of In a ___________________ experimental design,independent random samples...

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

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

The answer of \[\begin{array} { l l l l l...

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

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

The answer of A machine manufacturer conducted a study to...

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

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:

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.

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.

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?

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.