Deck 11: Analysis of Variance

Question 1

In a one-factor ANOVA analysis, the among sum of squares and within sum of
squares must add up to the total sum of squares.

Answer 1

True

Question 2

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that
Bumps the fewest mean number of passengers as possible during a month. An experiment is set
Up in which each package is used to make reservations for 5 randomly selected weeks. (A total of
20 weeks was included in the experiment.) The number of passengers bumped each week is given
Below. How should the data be analyzed?
Package 1: 12, 14, 9, 11, 16
Package 2: 2, 4, 7, 3, 1
Package 3: 10, 9, 6, 10, 12
Package 4: 7, 6, 6, 15, 12

A) F test for differences in variances.
B) One-way ANOVA F test.
C) t test for the differences in means.
D) t test for the mean difference.

Answer 2

B

Question 3

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, the among group degrees of freedom is

A) 3
B) 4
C) 12
D) 16

Answer 3

3

Question 4

If you are comparing the mean sales among 3 different brands you are dealing
with a three-way ANOVA design.

Question 5

When would you use the Tukey-Kramer procedure?

A) To test for normality.
B) To test for homogeneity of variance.
C) To test independence of errors.
D) To test for differences in pairs of means.

Question 6

SCENARIO 11-1
An airline wants to select a computer software package for its reservation system. Four software
packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps
as few passengers as possible during a month. An experiment is set up in which each package is used
to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the
experiment.) The number of passengers bumped each week is obtained, which gives rise to the
following Excel output: $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l c c c c c c } \hline \text { Source of Variation } & S S & d f & M S & F & P \text {-value } & F \text { crit } \\\hline \text { Between Groups } & 212.4 & 3 & & 8.304985 & 0.001474 & 3.238867 \\\text { Within Groups } & 136.4 & & 8.525 & & & \\& & & & & \\\text { Total } & 348.8 & & & & & \\\hline\end{array}\end{array}$$

-Referring to Scenario 11-1, at a significance level of 1%,

A) there is insufficient evidence to conclude that the mean number of customers bumped by the 4 packages are not all the same.
B) there is insufficient evidence to conclude that the mean number of customers bumped by the 4 packages are all the same.
C) there is sufficient evidence to conclude that the mean number of customers bumped by the 4 packages are not all the same.
D) there is sufficient evidence to conclude that the mean number of customers bumped by the 4 packages are all the same.

Question 7

A completely randomized design

A) has only one factor with several treatment groups.
B) can have more than one factor, each with several treatment groups.
C) has one factor and one block.
D) has one factor and one block and multiple values.

Question 8

The F test statistic in a one-way ANOVA is

A) MSW/MSA.
B) SSW/SSA.
C) MSA/MSW.
D) SSA/SSW.

Question 9

The analysis of variance (ANOVA) tests hypotheses about the population
variance.

Question 10

The degrees of freedom for the F test in a one-way ANOVA are

Question 11

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, the within group sum of squares is

A) 1.0606
B) 1.1825
C) 3.1819
D) 4.3644

Question 12

When the F test is used for ANOVA, the rejection region is always in the right tail.

Question 13

In a one-way ANOVA, the null hypothesis is always

A) there is no difference in the population means.
B) there is some treatment effect.
C) all the population means are different.
D) some of the population means are different.

Question 14

The MSE must always be positive.

Question 15

Which of the following components in an ANOVA table are not additive?

A) Sum of squares.
B) Degrees of freedom.
C) Mean squares.
D) It is not possible to tell.

Question 16

In a one-way ANOVA

A) an interaction term is present.
B) an interaction effect can be tested.
C) there is no interaction term.
D) the interaction term has (c - 1)(n - 1) degrees of freedom.

Question 17

SCENARIO 11-1
An airline wants to select a computer software package for its reservation system. Four software
packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps
as few passengers as possible during a month. An experiment is set up in which each package is used
to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the
experiment.) The number of passengers bumped each week is obtained, which gives rise to the
following Excel output: $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l c c c c c c } \hline \text { Source of Variation } & S S & d f & M S & F & P \text {-value } & F \text { crit } \\\hline \text { Between Groups } & 212.4 & 3 & & 8.304985 & 0.001474 & 3.238867 \\\text { Within Groups } & 136.4 & & 8.525 & & & \\& & & & & \\\text { Total } & 348.8 & & & & & \\\hline\end{array}\end{array}$$

-Referring to Scenario 11-1, the total degrees of freedom is

A) 3
B) 4
C) 16
D) 19

Question 18

In a one-way ANOVA, if the computed F statistic is greater than the critical F value you may

Question 19

SCENARIO 11-1
An airline wants to select a computer software package for its reservation system. Four software
packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps
as few passengers as possible during a month. An experiment is set up in which each package is used
to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the
experiment.) The number of passengers bumped each week is obtained, which gives rise to the
following Excel output: $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l c c c c c c } \hline \text { Source of Variation } & S S & d f & M S & F & P \text {-value } & F \text { crit } \\\hline \text { Between Groups } & 212.4 & 3 & & 8.304985 & 0.001474 & 3.238867 \\\text { Within Groups } & 136.4 & & 8.525 & & & \\& & & & & \\\text { Total } & 348.8 & & & & & \\\hline\end{array}\end{array}$$

-Referring to Scenario 11-1, the among-group (between-group) mean squares is

A) 8.525
B) 70.8
C) 212.4
D) 637.2

Question 20

SCENARIO 11-1
An airline wants to select a computer software package for its reservation system. Four software
packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps
as few passengers as possible during a month. An experiment is set up in which each package is used
to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the
experiment.) The number of passengers bumped each week is obtained, which gives rise to the
following Excel output: $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l c c c c c c } \hline \text { Source of Variation } & S S & d f & M S & F & P \text {-value } & F \text { crit } \\\hline \text { Between Groups } & 212.4 & 3 & & 8.304985 & 0.001474 & 3.238867 \\\text { Within Groups } & 136.4 & & 8.525 & & & \\& & & & & \\\text { Total } & 348.8 & & & & & \\\hline\end{array}\end{array}$$

-Referring to Scenario 11-1, the within groups degrees of freedom is

A) 3
B) 4
C) 16
D) 19

Question 21

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, what should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

A) Reject the null hypothesis because the p-value is smaller than the level of significance.
B) Reject the null hypothesis because the p-value is larger than the level of significance.
C) Do not reject the null hypothesis because the p-value is smaller than the level of significance.
D) Do not reject the null hypothesis because the p-value is larger than the level of significance.

Question 22

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, the within group variation or SSW is __________.

Question 23

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, the among group variation or SSA is __________.

Question 24

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, the test is less sensitive to the assumption that the
population of speeds has the same variance for the 4 brands because the sample sizes of the 4
brands are equal.

Question 25

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, the null hypothesis that the mean downhill coasting speeds of the 4
brands of bicycles are equal will be rejected at a level of significance of 0.05 if the value of the
test statistic is greater than __________.

Question 26

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, the critical value of Levene's test for homogeneity of variances at a 5% level of significance is

A) 0.64
B) 2.48
C) 3.29
D) 3.49

Question 27

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, the null hypothesis should be rejected at a 5% level of
significance.

Question 28

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

A) There is insufficient evidence that the variances are all the same.
B) There is sufficient evidence that the variances are all the same.
C) There is insufficient evidence that the variances are not all the same.
D) There is sufficient evidence that the variances are not all the same.

Question 29

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, the sporting goods retailer decided to perform an ANOVA F test.
The amount of total variation or SST is __________.

Question 30

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table:
Referring to Scenario 11-2, the null hypothesis for Levene's test for homogeneity of variances is

Question 31

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances at a 5% level of significance are, respectively,

A) 3, 12
B) 12, 3
C) 3, 15
D) 15, 3

Question 32

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, construct the ANOVA table from the sample data.

Question 33

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, the value of the test statistic for Levene's test for homogeneity of variances is

A) 0.25
B) 0.37
C) 4.36
D) 10.76

Question 34

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, the p-value of the test statistic for Levene's test for homogeneity of variances is

A) 0.25
B) 0.64
C) 0.86
D) 3.49

Question 35

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, the decision made implies that all 4 means are
significantly different.

Question 36

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2, the within group mean squares is

A) 0.0985
B) 0.2910
C) 1.0606
D) 1.1825

Question 37

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, the test is valid only if the population of speeds has the
same variance for the 4 brands.

Question 38

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, the value of MSA is __________, while MSW is __________.

Question 39

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, in testing the null hypothesis that the mean downhill coasting speeds
of the 4 brands of bicycles are equal, the value of the test statistic is __________.

Question 40

SCENARIO 11-2
A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four
neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and
the ratios recorded for each, as shown below.
A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3
B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table: $$\begin{array} { l c c l c l } \hline \text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR } > \text { F } \\\hline \text { Neighborhoods } & & 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & & \\\text { Total } & & 4.3644 & & & \\\hline\end{array}$$

-Referring to Scenario 11-2,

A) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not all the same.
B) at the 0.01 level of significance, the mean ratios for the 4 neighborhoods are all the same.
C) at the 0.10 level of significance, the mean ratios for the 4 neighborhoods are not significantly different.
D) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not significantly different from 0.

Question 41

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, the test is valid only if the population of speeds is
normally distributed.

Question 42

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, the within-group variation or SSW is __________.

Question 43

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, the among-group variation or SSA is __________.

Question 44

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, based on the Tukey-Kramer procedure with an overall
level of significance of 0.05, the retailer would decide that there is no significant difference
between any pair of mean speeds.

Question 45

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, what is the p-value of the test statistic for Levene's test for
homogeneity of variances?

Question 46

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, what is the value of the test statistic for Levene's test for
homogeneity of variances?

Question 47

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, what should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

A) Reject the null hypothesis because the p-value is smaller than the level of significance.
B) Reject the null hypothesis because the p-value is larger than the level of significance.
C) Do not reject the null hypothesis because the p-value is smaller than the level of significance.
D) Do not reject the null hypothesis because the p-value is larger than the level of significance.

Question 48

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

A) There is insufficient evidence that the variances are all the same.
B) There is sufficient evidence that the variances are all the same.
C) There is insufficient evidence that the variances are not all the same.
D) There is sufficient evidence that the variances are not all the same.

Question 49

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, the null hypothesis for Levene's test for homogeneity of variances is

Question 50

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, the test is robust to the violation of the assumption that
the population of speeds is normally distributed.

Question 51

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, the sporting goods retailer decided to compare the 4 treatment means
by using the Tukey-Kramer procedure with an overall level of significance of 0.05. There are
________ pairwise comparisons that can be made.

Question 52

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, using an overall level of significance of 0.05, the critical value of the
Studentized range Q used in calculating the critical range for the Tukey-Kramer procedure is
________.

Question 53

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, based on the Tukey-Kramer procedure with an overall
level of significance of 0.05, the retailer would decide that there is a significant difference
between all pairs of mean speeds.

Question 54

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, based on the Tukey-Kramer procedure with an overall
level of significance of 0.05, the retailer would decide that the 3 means other than the mean for
Tornado are not significantly different from each other.

Question 55

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, using an overall level of significance of 0.05, the critical range for the
Tukey-Kramer procedure is ________.

Question 56

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below. $$\begin{array} { ccccc} \underline{\text { Trial }} & \underline{\text { Barth } }& \underline{ \text { Tornado } }& \underline{\text { Reiser }} & \underline{ \text { Shaw }} \\1 & 43 & 37 & 41 &43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$$

-Referring to Scenario 11-3, based on the Tukey-Kramer procedure with an overall
level of significance of 0.05, the retailer would decide that the mean speed for the Tornado brand
is significantly different from each of the mean speeds for other brands.

Question 57

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, the agronomist decided to perform an ANOVA F test. The amount of
total variation or SST is __________.

Question 58

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, the value of MSA is __________, while MSW is __________.

Question 59

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, what is the critical value of Levene's test for homogeneity of
variances at a 5% level of significance?

Question 60

SCENARIO 11-3
As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting
speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill
speeds. The results are presented in miles per hour in the table below.
Referring to Scenario 11-3, what are the numerator and denominator degrees of freedom for
Levene's test for homogeneity of variances respectively?

Question 61

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, state the null hypothesis that can be tested.

Question 62

SCENARIO 11-5
A hotel chain has identically small sized resorts in 5 locations in different small islands. The data that
follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations.
Referring to Scenario 11-5, the among-group variation or SSA is _________.

Question 63

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows. $\begin{array}{cccc} \underline{\text { Trial }} & \underline{\text { Smith } }& \underline{ \text {Walsh } }& \underline{\text { Trevor }} \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$


-Referring to Scenario 11-4, the null hypothesis should be rejected at 0.005 level of
significance.

Question 64

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, the value of the test statistic is __________.

Question 65

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows. $\begin{array}{cccc} \underline{\text { Trial }} & \underline{\text { Smith } }& \underline{ \text {Walsh } }& \underline{\text { Trevor }} \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$


-Referring to Scenario 11-4, the test is valid only if the population of crop yields
has the same variance for the 3 varieties.

Question 66

SCENARIO 11-5
A hotel chain has identically small sized resorts in 5 locations in different small islands. The data that
follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. $$\begin{array}{l}\begin{array} { l c c c c c } \underline { \text { ROW } } & \underline{ \text { Location A }} & \underline{ \text { Location B} } & \underline{ \text { Location C} } & \underline{\text { Location D} } & \underline{\text { Location E }} \\1 & 28 & 40 & 21 & 37 & 2 \\2 & 33 & 35 & 21 & 47 & 19 \\3 & 41 & 33 & 27 & 45 & 25\end{array}\\\\\text { Analysis of Variance }\\\begin{array} { l r r c c c } \hline \text { Source } & { d f } & \text { SS } & \text { MS } & F & p \\\hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\\text { Error } & 10 & 210.0 & & & \\\text { Total } & & & & & \\\hline\end{array}\end{array}$$

-Referring to Scenario 11-5, if a level of significance of 0.05 is chosen, the null
hypothesis should be rejected.

Question 67

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows. $\begin{array}{cccc} \underline{\text { Trial }} & \underline{\text { Smith } }& \underline{ \text {Walsh } }& \underline{\text { Trevor }} \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$


-Referring to Scenario 11-4, based on the Tukey-Kramer procedure with an overall
level of significance of 0.01, the agronomist would decide that there is a significant difference
between the crop yield of Smith and Walsh seeds.

Question 68

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows. $\begin{array}{cccc} \underline{\text { Trial }} & \underline{\text { Smith } }& \underline{ \text {Walsh } }& \underline{\text { Trevor }} \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$


-Referring to Scenario 11-4, the decision made at 0.005 level of significance
implies that all 3 means are significantly different.

Question 69

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, using an overall level of significance of 0.01, the critical value of the
Studentized range Q used in calculating the critical range for the Tukey-Kramer procedure is
________.

Question 70

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, the null hypothesis will be rejected at a level of significance of 0.01 if
the value of the test statistic is greater than __________.

Question 71

SCENARIO 11-5
A hotel chain has identically small sized resorts in 5 locations in different small islands. The data that
follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. $$\begin{array}{l}\begin{array} { l c c c c c } \underline { \text { ROW } } & \underline{ \text { Location A }} & \underline{ \text { Location B} } & \underline{ \text { Location C} } & \underline{\text { Location D} } & \underline{\text { Location E }} \\1 & 28 & 40 & 21 & 37 & 2 \\2 & 33 & 35 & 21 & 47 & 19 \\3 & 41 & 33 & 27 & 45 & 25\end{array}\\\\\text { Analysis of Variance }\\\begin{array} { l r r c c c } \hline \text { Source } & { d f } & \text { SS } & \text { MS } & F & p \\\hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\\text { Error } & 10 & 210.0 & & & \\\text { Total } & & & & & \\\hline\end{array}\end{array}$$

-Referring to Scenario 11-5, if a level of significance of 0.05 is chosen, the decision
made indicates that all 5 locations have different mean occupancy rates.

Question 72

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, construct the ANOVA table from the sample data.

Question 73

SCENARIO 11-5
A hotel chain has identically small sized resorts in 5 locations in different small islands. The data that
follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations.
Referring to Scenario 11-5, the within-group variation or SSW is _________.

Question 74

SCENARIO 11-5
A hotel chain has identically small sized resorts in 5 locations in different small islands. The data that
follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations.
Referring to Scenario 11-5, the total variation or SST is ________.

Question 75

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows. $\begin{array}{cccc} \underline{\text { Trial }} & \underline{\text { Smith } }& \underline{ \text {Walsh } }& \underline{\text { Trevor }} \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$


-Referring to Scenario 11-4, based on the Tukey-Kramer procedure with an overall
level of significance of 0.01, the agronomist would decide that there is a significant difference
between the crop yield of Smith and Trevor seeds.

Question 76

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, the agronomist decided to compare the 3 treatment means by using
the Tukey-Kramer procedure with an overall level of significance of 0.01. There are ________
pairwise comparisons that can be made.

Question 77

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows. $\begin{array}{cccc} \underline{\text { Trial }} & \underline{\text { Smith } }& \underline{ \text {Walsh } }& \underline{\text { Trevor }} \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$


-Referring to Scenario 11-4, based on the Tukey-Kramer procedure with an overall
level of significance of 0.01, the agronomist would decide that there is a significant difference
between the crop yield of Walsh and Trevor seeds.

Question 78

SCENARIO 11-5
A hotel chain has identically small sized resorts in 5 locations in different small islands. The data that
follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations. $$\begin{array}{l}\begin{array} { l c c c c c } \underline { \text { ROW } } & \underline{ \text { Location A }} & \underline{ \text { Location B} } & \underline{ \text { Location C} } & \underline{\text { Location D} } & \underline{\text { Location E }} \\1 & 28 & 40 & 21 & 37 & 2 \\2 & 33 & 35 & 21 & 47 & 19 \\3 & 41 & 33 & 27 & 45 & 25\end{array}\\\\\text { Analysis of Variance }\\\begin{array} { l r r c c c } \hline \text { Source } & { d f } & \text { SS } & \text { MS } & F & p \\\hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\\text { Error } & 10 & 210.0 & & & \\\text { Total } & & & & & \\\hline\end{array}\end{array}$$

-Referring to Scenario 11-5, if a level of significance of 0.05 is chosen, the decision
made indicates that at least 2 of the 5 locations have different mean occupancy rates.

Question 79

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows.
Referring to Scenario 11-4, using an overall level of significance of 0.01, the critical range for the
Tukey-Kramer procedure is ________.

Question 80

SCENARIO 11-4
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields,
5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a
completely randomized design, the results are presented in the table that follows. $\begin{array}{cccc} \underline{\text { Trial }} & \underline{\text { Smith } }& \underline{ \text {Walsh } }& \underline{\text { Trevor }} \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$


-Referring to Scenario 11-4, the test is valid only if the population of crop yields is
normally distributed for the 3 varieties.