Question 1

For a disordinal interaction, the main effects can be interpreted independently of each
other.

Accepted Answer

A) True 
 B)False

Question 2

When there is one independent variable, the analysis of variance is called a
ANOVA.

Accepted Answer

The answer of When there is one independent variable, the...

Question 3

The manager of a grocery store wants to determine if there is a difference in the amount of money that the store brings in at different times of the day for different days of the week. The amount of money spent by five randomly selected customers is listed below. Analyze the data using a two-way ANOVA at $\alpha = 0.05$. $$\begin{array} { c | c c } 
& \text { Wednesday } & \text { Saturday } \
\hline \text { Morning } & 85 & 175 \
& 120 & 112 \
& 65 & 78 \
\text { Afternoon } & 95 & 130 \
& 60 & 80 \
& 110 & 160 \
& 150 & 150 \
\multirow{5}{*} { \text { Evening } } & 99 & 148 \
& 120 & 152 \
& 100 & 120 \
& 50 & 65 \
& 53 & 85 \
& 26 & 72 \
& 48 & 83 \
& 23 & 59
\end{array}$$

Accepted Answer

@#IMG-DLM& crit
2611

Question 4

In an Analysis of Variance Summary Table, if the Mean Square Between = 41 and the Mean Square Within = 27, then the null hypothesis of the groups having the same mean
Is

Accepted Answer

A)  rejected because 41 > 27. 
B)  cannot be determined without knowing the Sums of Squares (between and within). 
C)  accepted because 41 > 27. 
D)  cannot be determined without knowing the Degrees of Freedom (between and within). 
A)  rejected because 41 > 27. 
B)  cannot be determined without knowing the Sums of Squares (between and within). 
C)  accepted because 41 > 27. 
D)  cannot be determined without knowing the Degrees of Freedom (between and within).

Question 5

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
$\begin{array} { l r r r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \ \text { Soil Mixture } & 2 & 18.962963 & 9.481481 & 5.22449 & 0.01625 \ \text { Hybrid Variety } & 2 & 7.62963 & 3.814815 & 2.102041 & 0.151202 \ \text { Interaction } & 4 & 6.37037 & 1.592593 & 0.877551 & 0.496728 \ \text { Error } & 18 & 32.666667 & 1.814815 & & \ \text { Total } & 26 & 65.62963 & & & \end{array}$
Can the mean effect of the hybrid variety be interpreted? If so, interpret the main effect. $\mathrm { L }$ $\alpha = 0.01$ 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 6

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 you reject the hypothesis of no interactions?

Accepted Answer

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

Question 7

$$\text { An } F \text {-test can be used to compare the variances of three or more means. }$$

Accepted Answer

A) True 
 B)False

Question 8

Complete the formula for the Tukey test: $q =$

Accepted Answer

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

Question 9

In 2-way ANOVA, each independent variable investigated could have two or
more different treatments or .

Accepted Answer

The answer of In 2-way ANOVA, each independent variable investigated...

Question 10

Which of the following assumptions does not apply to the two-way ANOVA?

Accepted Answer

A)  The means of the populations must be equal. 
B)  The populations from which the samples were obtained must be normally or approximately normally distributed. 
C)  The samples must be independent of each other. 
D)  The groups must be equal in sample size. 
A)  The means of the populations must be equal. 
B)  The populations from which the samples were obtained must be normally or approximately normally distributed. 
C)  The samples must be independent of each other. 
D)  The groups must be equal in sample size.

Question 11

A portion of an ANOVA summary table is shown below. Calculate the $F$-test value.
$\begin{array} { l c c } \text { Source } & \text { Sum of Squares } & \text { Degrees of Freedom } \ \text { Between } & 16 & 2 \ \text { Within (error) } & 43 & 31 \ \text { Total } & 59 \end{array}$

Accepted Answer

A)  $5.77$ 
B)  $0.17$ 
C)  $41.66$ 
D)  $0.37$ 
A)  $5.77$ 
B)  $0.17$ 
C)  $41.66$ 
D)  $0.37$

Question 12

When the absolute value of $q$ is less than the critical value for the Tukey test, there is a significant difference between the two means being compared.

Accepted Answer

A) True 
 B)False

Question 13

An agricultural scientist performs a 2-way ANOVA to determine the effects of thr different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following MINITAB output presents the results.
Analysis of Variance for Sprouting
$\begin{array} { l r r r r } \text { Source } & \text { DF } & \text { SS } & \mathrm { MS } & \mathrm { F } \ \text { Soil Mixture } & 2 & 18.296296 & 9.148148 & 5.369565 \ \text { Hybrid Variety } & 2 & 4.740741 & 2.37037 & 1.391304 \ \text { Interaction } & 4 & 10.814815 & 2.703704 & 1.586957 \ \text { Error } & 18 & 30.666667 & 1.703704 & \ \text { Total } & 26 & 64.518519 & & \ \quad \text { P } & & & & \ 0.014832 & & & \ 0.274253 & & & \ 0.220746 & & & \end{array}$
i). Can you reject the hypothesis of no interactions?
ii). Can the mean effect of the soil mixture be interpreted? If so, interpret the main Use the $\alpha = 0.05$ level of significance.
iii). Can the mean effect of the hybrid variety be interpreted? If so, interpret the $m$ : effect. Use the $\alpha = 0.05$ level of significance.

Accepted Answer

i). No.
ii). Yes. Re

Question 14

In order to conduct the Scheffé test, one must compare the means two at a time using all
possible combinations of means.

Accepted Answer

A) True 
 B)False

Question 15

A diet center wanted to test three different methods for losing weight to determine if the average weight loss (reported in pounds/week) for each method is the same. The results for the three methods are tabulated below. Given that there is a significant difference between the three methods, use the Tukey test to determine if there is a significant difference between each pair of methods. Let $\alpha = 0.05$.
$\begin{array}{c|c|c}
\text { Liquid Diet (A) } & \text { Low-Calorie Diet (B) } & \text { Low-Calorie Diet and Exercise (C) } \
\hline 4 & 6 & 5 \
2 & 1 & 7 \
1 & 2 & 6 \
2 & 6 & 6 \
3 & 4 & 5
\end{array}$

Accepted Answer

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

Question 16

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 5 population means are not all equal. We should expect that

Accepted Answer

A)  at least 3 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test. 
B)  at least 5 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X }$, would be significant using the Scheffe test. 
C)  all 10 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test. 
D)  at least 1 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test. 
A)  at least 3 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test. 
B)  at least 5 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X }$, would be significant using the Scheffe test. 
C)  all 10 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test. 
D)  at least 1 of the comparisons of means $\bar { X } _ { i }$ versus $\bar { X } _ { j }$ would be significant using the Scheffe test.

Question 17

A researcher is performing a two-way ANOVA using two factors. The first factor has levels and the second factor has 3 levels. In the ANOVA Summary Table, the degrees of
Freedom for the first and second factors will be

Accepted Answer

A)  7 d.f. for the first factor and 3 d.f. for the second factor 
B)  8 d.f. for the first factor and 4 d.f. for the second factor 
C)  6 d.f. for the first factor and 2 d.f. for the second factor 
D)  21 d.f. for the first factor and 21 d.f. for the second factor 
A)  7 d.f. for the first factor and 3 d.f. for the second factor 
B)  8 d.f. for the first factor and 4 d.f. for the second factor 
C)  6 d.f. for the first factor and 2 d.f. for the second factor 
D)  21 d.f. for the first factor and 21 d.f. for the second factor

Question 18

In the Scheffe test, if $\bar { X } _ { 2 } = 8$ for a group size $n _ { 2 } = 8 , \bar { X } _ { 4 } = 13$ for a group size $n$ and the within-group variance $s _ { w } { } ^ { 2 } = 16$, then the $F _ { S }$ test value for comparing these two groups is equal to

Accepted Answer

A)  -1.25 
B)  3.91 
C)  6.25 
D)  1.56 
A)  -1.25 
B)  3.91 
C)  6.25 
D)  1.56

Question 19

If there are 6 means to be compared, then how many possible different comparisons (such as $\bar { X } _ { 2 }$ compared to $\bar { X } _ { 3 }$ ) are there altogether?

Accepted Answer

A)  15 
B)  30 
C)  6 
D)  36 
A)  15 
B)  30 
C)  6 
D)  36

Question 20

ANOVA is an abbreviation for the following term:

Accepted Answer

A)  Scheffé test 
B)  Tukey test 
C)  analysis of variance 
D)  variance 
A)  Scheffé test 
B)  Tukey test 
C)  analysis of variance 
D)  variance

For a disordinal interaction, the main effects can be interpreted independently of each other.

When there is one independent variable, the analysis of variance is called a ANOVA.

In an Analysis of Variance Summary Table, if the Mean Square Between = 41 and the Mean Square Within = 27, then the null hypothesis of the groups having the same mean Is

$\text { An } F \text {-test can be used to compare the variances of three or more means. }$

Complete the formula for the Tukey test: $q =$

In 2-way ANOVA, each independent variable investigated could have two or more different treatments or .

Which of the following assumptions does not apply to the two-way ANOVA?

A portion of an ANOVA summary table is shown below. Calculate the $F$ -test value. Source Sum of Squares Degrees of Freedom Between 16 2 Within (error) 43 31 Total 59

When the absolute value of $q$ is less than the critical value for the Tukey test, there is a significant difference between the two means being compared.

In order to conduct the Scheffé test, one must compare the means two at a time using all possible combinations of means.

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 5 population means are not all equal. We should expect that

A researcher is performing a two-way ANOVA using two factors. The first factor has levels and the second factor has 3 levels. In the ANOVA Summary Table, the degrees of Freedom for the first and second factors will be

In the Scheffe test, if $\bar { X } _ { 2 } = 8$ for a group size $n _ { 2 } = 8 , \bar { X } _ { 4 } = 13$ for a group size $n$ and the within-group variance $s _ { w } { } ^ { 2 } = 16$ , then the $F _ { S }$ test value for comparing these two groups is equal to

If there are 6 means to be compared, then how many possible different comparisons (such as $\bar { X } _ { 2 }$ compared to $\bar { X } _ { 3 }$ ) are there altogether?

ANOVA is an abbreviation for the following term:

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

For a disordinal interaction, the main effects can be interpreted independently of each other.

When there is one independent variable, the analysis of variance is called a ANOVA.

In an Analysis of Variance Summary Table, if the Mean Square Between = 41 and the Mean Square Within = 27, then the null hypothesis of the groups having the same mean Is

An F-test can be used to compare the variances of three or more means. \text { An } F \text {-test can be used to compare the variances of three or more means. } An F-test can be used to compare the variances of three or more means.

Complete the formula for the Tukey test: q=q =q=

In 2-way ANOVA, each independent variable investigated could have two or more different treatments or .

Which of the following assumptions does not apply to the two-way ANOVA?

A portion of an ANOVA summary table is shown below. Calculate the FFF -test value. Source Sum of Squares Degrees of Freedom Between 16 2 Within (error) 43 31 Total 59

When the absolute value of qqq is less than the critical value for the Tukey test, there is a significant difference between the two means being compared.

In order to conduct the Scheffé test, one must compare the means two at a time using all possible combinations of means.

Assume that the conclusion from an ANOVA is that the null hypothesis is rejected, in other words that the 5 population means are not all equal. We should expect that

A researcher is performing a two-way ANOVA using two factors. The first factor has levels and the second factor has 3 levels. In the ANOVA Summary Table, the degrees of Freedom for the first and second factors will be

If there are 6 means to be compared, then how many possible different comparisons (such as Xˉ2\bar { X } _ { 2 }Xˉ2​ compared to Xˉ3\bar { X } _ { 3 }Xˉ3​ ) are there altogether?

ANOVA is an abbreviation for the following term:

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

$\text { An } F \text {-test can be used to compare the variances of three or more means. }$

Complete the formula for the Tukey test: $q =$

A portion of an ANOVA summary table is shown below. Calculate the $F$ -test value. Source Sum of Squares Degrees of Freedom Between 16 2 Within (error) 43 31 Total 59

When the absolute value of $q$ is less than the critical value for the Tukey test, there is a significant difference between the two means being compared.

If there are 6 means to be compared, then how many possible different comparisons (such as $\bar { X } _ { 2 }$ compared to $\bar { X } _ { 3 }$ ) are there altogether?