Question 1

Complete the formula for the sum of squares between groups: $s _ { B } ^ { 2 } =$

Accepted Answer

A)  $\frac { \left( \bar { X } _ { i } - \bar { X } _ { j } \right) ^ { 2 } } { s _ { w } ^ { 2 } \left( 1 / n _ { \mathrm { i } } + 1 / n _ { j } \right) }$ 
B)  $\frac { \sum \left( n _ { i } - 1 \right) s _ { i } ^ { 2 } } { \sum \left( n _ { i } - 1 \right) }$ 
C)  $\frac { \bar { X } _ { i } - \bar { X } _ { j } } { \sqrt { s _ { w } ^ { 2 } / n } }$ 
D)  $\frac { \sum _ { i } n _ { i } \left( \bar { X } _ { i } - \bar { X } _ { G M } \right) ^ { 2 } } { k - 1 }$ 
A)  $\frac { \left( \bar { X } _ { i } - \bar { X } _ { j } \right) ^ { 2 } } { s _ { w } ^ { 2 } \left( 1 / n _ { \mathrm { i } } + 1 / n _ { j } \right) }$ 
B)  $\frac { \sum \left( n _ { i } - 1 \right) s _ { i } ^ { 2 } } { \sum \left( n _ { i } - 1 \right) }$ 
C)  $\frac { \bar { X } _ { i } - \bar { X } _ { j } } { \sqrt { s _ { w } ^ { 2 } / n } }$ 
D)  $\frac { \sum _ { i } n _ { i } \left( \bar { X } _ { i } - \bar { X } _ { G M } \right) ^ { 2 } } { k - 1 }$ D

Question 2

A Two-Way ANOVA Summary Table is shown below.
$\begin{array}{lrrrc}
\text { Source } &{\text { SS }} & \text { d.f. } & \text { MS } & \text { F } \
\text { Factor A } & 8.06 & 2 & 4.03 & 2.37 \
\text { Factor B } & 15.44 & 2 & 7.72 & 4.54 \
\text { Interaction A } \times \text { B } & 9.66 & 4 & 2.41 & 1.42 \
\text { Within (error) } & 45.90 & 27 & 1.7 & \
\text { Total } & 79.05 & 35 & &
\end{array}$
The critical value for the $F$-test using $\alpha = 0.05$, d.f.N. $= 2$, and d.f.D $= 27$ is $3.35$. Then,

Accepted Answer

A)  only the null hypothesis concerning Factor A should be rejected. 
B)  only the null hypothesis concerning Factor B should be rejected. 
C)  all of the null hypotheses should be accepted. 
D)  only the null hypothesis concerning Factor A and the Interaction (A ×
B)  effect should be rejected. 
A)  only the null hypothesis concerning Factor A should be rejected. 
B)  only the null hypothesis concerning Factor B should be rejected. 
C)  all of the null hypotheses should be accepted. 
D)  only the null hypothesis concerning Factor A and the Interaction (A ×
B)  effect should be rejected. B

Question 3

Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 8 , n _ { 2 } = 5$, and $n _ { 3 } = 9$. The sample means were $\bar { x } _ { 1 } = 1.61 , \bar { x } _ { 2 } = 2.09$, and $\bar { x } _ { 3 } = 1.50$. The sample standard deviations were $s _ { 1 } = 0.33 , s _ { 2 } = 0.25$, and $s _ { 3 } = 0.45$. The grand mean is $\bar { x } = 1.674091$.
Can you conclude that two or more of the population means are different? Use the $\alpha =$ of significance.

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No B

Question 4

$$\text { The value of the } F \text {-distribution can be negative. }$$

Accepted Answer

A) True 
 B)False

Question 5

A Two-Way ANOVA Summary Table is shown below.
$\begin{array}{lcrcc}
\text { Source } & \text { SS } & \text { d.f. } & \text { MS } & \text { F } \
\text { Factor A } & 6.05 & 2 & 3.02 & 2.16 \
\text { Factor B } & 3.78 & 2 & 1.89 & 1.35 \
\text { Interaction A } \times \text { B } & 7.90 & 4 & 1.97 & 1.41 \
\text { Within (error) } & 75.60 & 54 & 1.4 & \
\text { Total } & 93.324 & 62 & &
\end{array}$

The critical value for the $F$-test using $\alpha = 0.05$, d.f.N. $= 2$, and d.f.D $= 54$ is $3.17$. Then,

Accepted Answer

A)  The null hypothesis concerning Factor A should be rejected 
B)  The null hypothesis concerning Factor A and the Interaction (A × 
B)  effect should be rejected 
C)  The null hypothesis concerning Factor B should be rejected 
D)  All of the null hypotheses should be accepted 
A)  The null hypothesis concerning Factor A should be rejected 
B)  The null hypothesis concerning Factor A and the Interaction (A × 
B)  effect should be rejected 
C)  The null hypothesis concerning Factor B should be rejected 
D)  All of the null hypotheses should be accepted

Question 6

A researcher calculated the ANOVA summary table for an experiment, but accidentally spilled grape juice over the first line of the output. From the data below, calculate the test value.
Source
Sum of Squares d.f. Mean Square $F$
Between
$\begin{array} { l l l l } \text { Within (error) } & 174 & 43 & 4.05 \ \text { Total } & 230 & 47 & \end{array}$

Accepted Answer

A)  F = 0.91 
B)  F = 3.46 
C)  F = 1.32 
D)  F = 2.39 
A)  F = 0.91 
B)  F = 3.46 
C)  F = 1.32 
D)  F = 2.39

Question 7

The figure below is a result of a two-way ANOVA, which of the following statements wo apply?

Accepted Answer

A)  The graph does not give any indication of whether or not there is an interaction effect. 
B)  The main effects should not be interpreted without considering the interaction effect. 
C)  There is no significant interaction effect. 
D)  There is a significant interaction effect. 
A)  The graph does not give any indication of whether or not there is an interaction effect. 
B)  The main effects should not be interpreted without considering the interaction effect. 
C)  There is no significant interaction effect. 
D)  There is a significant interaction effect.

Question 8

In an Analysis of Variance Summary Table, if the Mean Square Between = 14 and the Mean Square Within = 27, then the null hypothesis of the groups having the same mean
Is

Accepted Answer

A)  cannot be determined without knowing the Degrees of Freedom (between and within). 
B)  accepted because 14 < 27. 
C)  cannot be determined without knowing the Sums of Squares (between and within). 
D)  rejected because 14 < 27. 
A)  cannot be determined without knowing the Degrees of Freedom (between and within). 
B)  accepted because 14 < 27. 
C)  cannot be determined without knowing the Sums of Squares (between and within). 
D)  rejected because 14 < 27.

Question 9

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubbes content.

Can you reject the hypothesis of no interactions?

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 10

Independent variables can also be called .

Accepted Answer

The answer of Independent variables can also be called ....

Question 11

$$\text { The } F \text {-test for comparing means is always right tailed. }$$

Accepted Answer

A) True 
 B)False

Question 12

An agricultural scientist performs a 2-way ANOVA to determine the effects of three diffe soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. following MINITAB output presents the results.
Analysis of Variance for Sprouting
$\begin{array} { l r r r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \ \text { Soil Mixture } & 2 & 16.962963 & 8.481481 & 4.320755 & 0.029337 \ \text { Hybrid Variety } & 2 & 3.185185 & 1.592593 & 0.811321 & 0.45987 \ \text { Interaction } & 4 & 13.925926 & 3.481481 & 1.773585 & 0.178159 \ \text { Error } & 18 & 35.333333 & 1.962963 & & \ \text { Total } & 26 & 69.407407 & & & \end{array}$
Can the mean effect of the soil mixture be interpreted? If so, interpret the main effect. Usi $\alpha = 0.05$ level of significance.

Accepted Answer

A)  Yes. Reject $H _ { 0 }$. 
B)  Yes. Do not reject $H _ { 0 }$. 
C)  No. 
A)  Yes. Reject $H _ { 0 }$. 
B)  Yes. Do not reject $H _ { 0 }$. 
C)  No.

Question 13

In a two-way ANOVA procedure, variable A has four levels and variable B has two
levels. The d.f.N. for factor A × B would be 3.

Accepted Answer

A) True 
 B)False

Question 14

The between-group variance and the within-group variance are sometimes referred to as

Accepted Answer

A)  mean squares. 
B)  main effects. 
C)  interaction effects. 
D)  an ANOVA summary table. 
A)  mean squares. 
B)  main effects. 
C)  interaction effects. 
D)  an ANOVA summary table.

Question 15

An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond apart. For each combination of curing time and curing temperature, three tests are performed. The results of the experiment are shown below.

Can the main effect of curing temperature (low or high) on bonding strength be interprete interpret the main effect using the $\alpha = 0.01$ level of significance.

Accepted Answer

A)  Yes. Do not reject $H _ { 0 }$. 
B)  Yes. Reject $H _ { 0 }$. 
C)  No. 
A)  Yes. Do not reject $H _ { 0 }$. 
B)  Yes. Reject $H _ { 0 }$. 
C)  No.

Question 16

An experiment is conducted to study the effects of curing times and curing temperatures on the bonding strength of an epoxy adhesive. In the experiment, two steel rods are adhered together end-to-end, and the bonding strength is defined as the force, in pounds, required to pull the bond apart. For each combination of curing time and curing temperature, three tests are performed. The results of the experiment are shown below.

Can the main effect of curing time on bonding strength be interpreted? If so, interpret the main effect. using the $\alpha = 0.01$ level of significance.

Accepted Answer

A)  Yes. Reject $H _ { 0 }$. 
B)  Yes. Do not reject $H _ { 0 }$. 
C)  No. 
A)  Yes. Reject $H _ { 0 }$. 
B)  Yes. Do not reject $H _ { 0 }$. 
C)  No.

Question 17

To find the critical value for the Tukey test, the number of means, $k$, and the degrees of freedom associated with the between group variance, $V$, are needed.

Accepted Answer

A) True 
 B)False

Question 18

The head of the English department wants to determine if the average number of students an English course differs depending upon the time of day that the course is being offered.
$\begin{array}{ccc}
\hline \text { Morning } & \text { Afternoon } & \text { Evening } \
\hline 25 & 25 & 27 \
26 & 24 & 26 \
27 & 18 & 24 \
26 & 20 & 23 \
27 & 23 & 25 \
\hline
\end{array}$

Is there a significant difference between the mean attendance for the classes given for $\alpha = 0.05$ ?

Accepted Answer

A)  The $F$-test cannot be used to answer whether or not there is a significant difference between the means. 
B)  No, there is no significant difference between the means. 
C)  Yes, there is a significant difference between the means. 
A)  The $F$-test cannot be used to answer whether or not there is a significant difference between the means. 
B)  No, there is no significant difference between the means. 
C)  Yes, there is a significant difference between the means.

Question 19

Which of the following assumptions is not made for the $F$-test for comparing three or more means?

Accepted Answer

A)  The variances of the populations must be equal. 
B)  The samples must be independent of each other. 
C)  The sample sizes must be equal. 
D)  The populations from which the samples were obtained must be normally distributed. 
A)  The variances of the populations must be equal. 
B)  The samples must be independent of each other. 
C)  The sample sizes must be equal. 
D)  The populations from which the samples were obtained must be normally distributed.

Question 20

The data consist of the weights in ounces of three different types of digital camera. Use $\alpha = 0.05$ to see if the means are equal.
$\begin{array}{c|c|c}
\text { 2-3 Megapixels } & \text { 4-5 Megapixels } & \text { 6-8 Megapixels } \
\hline 7 & 17 & 26 \
9 & 14 & 21 \
9 & 10 & 25 \
11 & 18 & 24 \
12 & 12 & 22
\end{array}$

Accepted Answer

\[\begin{array} { l } 
q _ { \text {crit

Complete the formula for the sum of squares between groups: $s _ { B } ^ { 2 } =$

$\text { The value of the } F \text {-distribution can be negative. }$

A researcher calculated the ANOVA summary table for an experiment, but accidentally spilled grape juice over the first line of the output. From the data below, calculate the test value. Source Sum of Squares d.f. Mean Square $F$ Between Within (error) 174 43 4.05 Total 230 47

The figure below is a result of a two-way ANOVA, which of the following statements wo apply?

In an Analysis of Variance Summary Table, if the Mean Square Between = 14 and the Mean Square Within = 27, then the null hypothesis of the groups having the same mean Is

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubbes content. Can you reject the hypothesis of no interactions?

Independent variables can also be called .

$\text { The } F \text {-test for comparing means is always right tailed. }$

In a two-way ANOVA procedure, variable A has four levels and variable B has two levels. The d.f.N. for factor A × B would be 3.

The between-group variance and the within-group variance are sometimes referred to as

To find the critical value for the Tukey test, the number of means, $k$ , and the degrees of freedom associated with the between group variance, $V$ , are needed.

Which of the following assumptions is not made for the $F$ -test for comparing three or more means?

The data consist of the weights in ounces of three different types of digital camera. Use $\alpha = 0.05$ to see if the means are equal. 2-3 Megapixels 4-5 Megapixels 6-8 Megapixels 7 17 26 9 14 21 9 10 25 11 18 24 12 12 22

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Nonparametric Statistics

Sampling and Simulation

Filters

Exam 12: Analysis of Variance

Complete the formula for the sum of squares between groups: sB2=s _ { B } ^ { 2 } =sB2​=

The value of the F-distribution can be negative. \text { The value of the } F \text {-distribution can be negative. } The value of the F-distribution can be negative.

A researcher calculated the ANOVA summary table for an experiment, but accidentally spilled grape juice over the first line of the output. From the data below, calculate the test value. Source Sum of Squares d.f. Mean Square FFF Between Within (error) 174 43 4.05 Total 230 47

The figure below is a result of a two-way ANOVA, which of the following statements wo apply?

In an Analysis of Variance Summary Table, if the Mean Square Between = 14 and the Mean Square Within = 27, then the null hypothesis of the groups having the same mean Is

The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubbes content. Can you reject the hypothesis of no interactions?

Independent variables can also be called .

The F-test for comparing means is always right tailed. \text { The } F \text {-test for comparing means is always right tailed. } The F-test for comparing means is always right tailed.

In a two-way ANOVA procedure, variable A has four levels and variable B has two levels. The d.f.N. for factor A × B would be 3.

The between-group variance and the within-group variance are sometimes referred to as

To find the critical value for the Tukey test, the number of means, kkk , and the degrees of freedom associated with the between group variance, VVV , are needed.

Which of the following assumptions is not made for the FFF -test for comparing three or more means?

The data consist of the weights in ounces of three different types of digital camera. Use α=0.05\alpha = 0.05α=0.05 to see if the means are equal. 2-3 Megapixels 4-5 Megapixels 6-8 Megapixels 7 17 26 9 14 21 9 10 25 11 18 24 12 12 22

The Nature of Probability and Statistics

Frequency Distributions and Graphs

Data Description

Probability and Counting Rules

Discrete Probability Distributions

The Normal Distribution

Confidence Intervals and Sample Size

Hypothesis Testing

Testing the Difference Between Two Means, Two Variances, and Two Proportions

Correlation and Regression

Other Chi-Square Tests

Nonparametric Statistics

Sampling and Simulation

Filters

Complete the formula for the sum of squares between groups: $s _ { B } ^ { 2 } =$

$\text { The value of the } F \text {-distribution can be negative. }$

A researcher calculated the ANOVA summary table for an experiment, but accidentally spilled grape juice over the first line of the output. From the data below, calculate the test value. Source Sum of Squares d.f. Mean Square $F$ Between Within (error) 174 43 4.05 Total 230 47

$\text { The } F \text {-test for comparing means is always right tailed. }$

To find the critical value for the Tukey test, the number of means, $k$ , and the degrees of freedom associated with the between group variance, $V$ , are needed.

Which of the following assumptions is not made for the $F$ -test for comparing three or more means?

The data consist of the weights in ounces of three different types of digital camera. Use $\alpha = 0.05$ to see if the means are equal. 2-3 Megapixels 4-5 Megapixels 6-8 Megapixels 7 17 26 9 14 21 9 10 25 11 18 24 12 12 22