Deck 11: Analysis of Variance

Question 1

The F test statistic in a one-way ANOVA is

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

Answer 1

MSA/MSW.

Question 2

The MSE must always be positive.

Answer 2

True

Question 3

Instruction 11-2
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 as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for five 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 Microsoft
$$\begin{array}{l}\text { ANOVA }\\\begin{array} { | l | l | l | l | l |l| l | } \hline \text { Source of Variation } & \text { SS } & d f & \text { MS } & F & P \text {-value } & F \text { crit } \\\hline \text { Between Groups } & 212.4 & 3 & & 8.304985 & 0.001474 & 3.238867 \\\hline \text { Within Groups } & 136.4 & & 8.525 & & & \\\hline & & & & & & \\\hline \text { Total } & 348.8 & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-2,the within groups degrees of freedom is

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

Answer 3

16.

Question 4

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

Question 5

One-way ANOVA is used

A)when analysing a numerical variable.
B)to analyse the variation between and within the groups.
C)to compare the means of the groups.
D)All of the above.

Question 6

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

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

Question 7

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 five 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 analysed? 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 mean difference.
D)t test for the differences in means.

Question 8

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

A)not reject H₀ because a mistake has been made.
B)reject H₀ since there is evidence all the means differ.
C)reject H₀ since there is evidence of a treatment effect.
D)not reject H₀ since there is no evidence of a difference.

Question 9

A completely randomised design

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

Question 10

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

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

Question 11

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.

Question 12

Referring to Instruction 11-7,the total mean squares is 261.90.

Question 13

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

Question 14

In a one-way ANOVA,

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

Question 15

The F test in a completely randomised model is just an expansion of the t test for independent samples.

Question 16

When would you use the Tukey-Kramer procedure?

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

Question 17

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

Question 18

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

A)(c - 1)and (n - c).
B)(n - 1)and (c - n).
C)(c - n)and (n - 1).
D)(n - c)and (c - 1).

Question 19

Instruction 11-2
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 as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for five 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 Microsoft
$$\begin{array}{l}\text { ANOVA }\\\begin{array} { | l | l | l | l | l |l| l | } \hline \text { Source of Variation } & \text { SS } & d f & \text { MS } & F & P \text {-value } & F \text { crit } \\\hline \text { Between Groups } & 212.4 & 3 & & 8.304985 & 0.001474 & 3.238867 \\\hline \text { Within Groups } & 136.4 & & 8.525 & & & \\\hline & & & & & & \\\hline \text { Total } & 348.8 & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-2,the total degrees of freedom is

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

Question 20

A completely randomised design with four groups would have six possible pairwise comparisons.

Question 21

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,the decision made implies that all four means are significantly different.

Question 22

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 11-3,the among group degrees of freedom is

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

Question 23

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 11-3,the critical value of Levene's test for homogeneity of variances at a 5% level of significance is

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

Question 24

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 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 not sufficient evidence that the variances are not all the same.
B)There is not sufficient evidence that the variances are all the same.
C)There is sufficient evidence that the variances are not all the same.
D)There is sufficient evidence that the variances are all the same.

Question 25

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 11-3,the p-value of the test statistic for Levene's test for homogeneity of variances is

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

Question 26

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

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

Question 27

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

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

Question 28

Instruction 11-2
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 as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for five 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 Microsoft
$$\begin{array}{l}\text { ANOVA }\\\begin{array} { | l | l | l | l | l |l| l | } \hline \text { Source of Variation } & \text { SS } & d f & \text { MS } & F & P \text {-value } & F \text { crit } \\\hline \text { Between Groups } & 212.4 & 3 & & 8.304985 & 0.001474 & 3.238867 \\\hline \text { Within Groups } & 136.4 & & 8.525 & & & \\\hline & & & & & & \\\hline \text { Total } & 348.8 & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-2,the among-group (between-group)mean squares is

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

Question 29

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 11-3,the within group mean squares is

A)1.06.
B)0.10.
C)0.29.
D)1.18.

Question 30

Instruction 11-2
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 as few passengers as possible during a month.An experiment is set up in which each package is used to make reservations for five 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 Microsoft
$$\begin{array}{l}\text { ANOVA }\\\begin{array} { | l | l | l | l | l |l| l | } \hline \text { Source of Variation } & \text { SS } & d f & \text { MS } & F & P \text {-value } & F \text { crit } \\\hline \text { Between Groups } & 212.4 & 3 & & 8.304985 & 0.001474 & 3.238867 \\\hline \text { Within Groups } & 136.4 & & 8.525 & & & \\\hline & & & & & & \\\hline \text { Total } & 348.8 & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-2,at a significance level of 1%,

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

Question 31

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,what should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

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

Question 32

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,the test is less sensitive to the assumption that the population of speeds has the same variance for the four brands if the sample sizes of the four brands are equal.

Question 33

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,the null hypothesis should be rejected at a 5% level of significance.

Question 34

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,the test is valid only if the population of speeds is normally distributed.

Question 35

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 11-3,the value of the test statistic for Levene's test for homogeneity of variances is

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

Question 36

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 11-3,

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

Question 37

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,the test is valid only if the population of speeds has the same variance for the four brands.

Question 38

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,the test is robust to the violation of the assumption that the population of speeds is the normally distributed.

Question 39

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 11-3,the within group sum of squares is

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

Question 40

Instruction 11-3
A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighbourhoods (A,B,C,and D).Four properties are randomly selected from each neighbourhood 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 summarised in the following table:
$\begin{array}{llclcl}\text { Source } & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { PR }>\text { F } \\\hline \text { Neighbourhoods } && 3.1819 & 1.0606 & 10.76 & 0.001 \\\text { Error } & 12 & & & &\\total&&4.3644\end{array}$

-Referring to Instruction 11-3,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)15,3
D)3,15

Question 41

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,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 42

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { ROW } & \text { Caymen } & \text { Pennkapmp } & \text { California } & \text { Mayaguez } & \text { Maui } \\\hline 1 & 28 & 40 & 21 & 37 & 22 \\\hline 2 & 33 & 35 & 21 & 47 & 19 \\\hline 3 & 41 & 33 & 27 & 45 & 25 \\\hline\end{array}$$ $$\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l r r r r r } \hline \text { Source } & d f & \text { SS } & \text { MS } & F & p \\\hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\\text { Error } & 10 & 210.0 & & & \\\text { Total } & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-7,if a level of significance of 0.05 is chosen,the null hypothesis should be rejected.

Question 43

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,the within group variation or SSW is ________.

Question 44

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,in testing the null hypothesis that the average downhill coasting speeds of the four brands of bicycles are equal,the value of the test statistic is ________.

Question 45

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,what is the value of the test statistic for Levene's test for homogeneity of variances?

Question 46

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,using an overall level of significance of 0.05,the critical value of the Studentised range Q used in calculating the critical range for the Tukey-Kramer procedure is ________.

Question 47

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,the value of MSA is ________,while MSW is ________.

Question 48

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,the sporting goods retailer decided to compare the four 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 49

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,using an overall level of significance of 0.05,the critical range for the Tukey-Kramer procedure is ________.

Question 50

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,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 51

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

Question 52

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,the null hypothesis that the average downhill coasting speeds of the four 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 53

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,the sporting goods retailer decided to perform an ANOVA F test.The amount of total variation or SST is ________.

Question 54

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,construct the ANOVA table from the sample data.

Question 55

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,what are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

Question 56

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { ROW } & \text { Caymen } & \text { Pennkapmp } & \text { California } & \text { Mayaguez } & \text { Maui } \\\hline 1 & 28 & 40 & 21 & 37 & 22 \\\hline 2 & 33 & 35 & 21 & 47 & 19 \\\hline 3 & 41 & 33 & 27 & 45 & 25 \\\hline\end{array}$$ $$\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l r r r r r } \hline \text { Source } & d f & \text { SS } & \text { MS } & F & p \\\hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\\text { Error } & 10 & 210.0 & & & \\\text { Total } & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-7,if a level of significance of 0.05 is chosen,the decision made indicates that all five locations have different mean occupancy rates.

Question 57

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,based on the Tukey-Kramer procedure with an overall level of significance of 0.05,the retailer would decide that the three means other than the mean for Tornado are not significantly different from each other.

Question 58

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,the among group variation or SSA is ________.

Question 59

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.

Referring to Instruction 11-6,what is the p-value of the test statistic for Levene's test for homogeneity of variances?

Question 60

Instruction 11-6
As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She recorded three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below.
$\begin{array}{lcccc}\text { Trial } & \frac{\text { Barth }}{} & \frac{\text { Tomado }}{} & \frac{\text { Reiser }}{} & \frac{\text { Shaw }}{} \\1 & 43 & 37 & 41 & 43 \\2 & 46 & 38 & 45 & 45 \\3 & 43 & 39 & 42 & 46\end{array}$

-Referring to Instruction 11-6,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 61

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,what is the value of the test statistic for Levene's test for homogeneity of variances?

Question 62

Instruction 11-9
An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows.

Referring to Instruction 11-9,the within-group variation or SSW is ________.

Question 63

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,the value of MSA is ________ while MSW is ________.

Question 64

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

Question 65

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { ROW } & \text { Caymen } & \text { Pennkapmp } & \text { California } & \text { Mayaguez } & \text { Maui } \\\hline 1 & 28 & 40 & 21 & 37 & 22 \\\hline 2 & 33 & 35 & 21 & 47 & 19 \\\hline 3 & 41 & 33 & 27 & 45 & 25 \\\hline\end{array}$$ $$\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l r r r r r } \hline \text { Source } & d f & \text { SS } & \text { MS } & F & p \\\hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\\text { Error } & 10 & 210.0 & & & \\\text { Total } & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-7,if a level of significance of 0.05 is chosen,the decision made indicates that at least two of the five locations have different mean occupancy rates.

Question 66

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,the numerator and denominator degrees of freedom of the test ratio are ________ and ________,respectively.

Question 67

Instruction 11-8
An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows.

Referring to Instruction 11-8,construct the ANOVA table from the sample data.

Question 68

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,the total variation or SST is ________.

Question 69

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,what is the p-value of the test statistic for Levene's test for homogeneity of variances?

Question 70

Instruction 11-9
An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows.

Referring to Instruction 11-9,using an overall level of significance of 0.01,the critical value of the Studentised range Q used in calculating the critical range for the Tukey-Kramer procedure is ________.

Question 71

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { ROW } & \text { Caymen } & \text { Pennkapmp } & \text { California } & \text { Mayaguez } & \text { Maui } \\\hline 1 & 28 & 40 & 21 & 37 & 22 \\\hline 2 & 33 & 35 & 21 & 47 & 19 \\\hline 3 & 41 & 33 & 27 & 45 & 25 \\\hline\end{array}$$ $$\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l r r r r r } \hline \text { Source } & d f & \text { SS } & \text { MS } & F & p \\\hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\\text { Error } & 10 & 210.0 & & & \\\text { Total } & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-7,what should be the conclusion for the Levene's test for homogeneity of variances at a 5% level of significance?

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

Question 72

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { ROW } & \text { Caymen } & \text { Pennkapmp } & \text { California } & \text { Mayaguez } & \text { Maui } \\\hline 1 & 28 & 40 & 21 & 37 & 22 \\\hline 2 & 33 & 35 & 21 & 47 & 19 \\\hline 3 & 41 & 33 & 27 & 45 & 25 \\\hline\end{array}$$ $$\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l r r r r r } \hline \text { Source } & d f & \text { SS } & \text { MS } & F & p \\\hline \text { Location } & 4 & 963.6 & & 11.47 & 0.001 \\\text { Error } & 10 & 210.0 & & & \\\text { Total } & & & & & \\\hline\end{array}\end{array}$$

-Referring to Instruction 11-7,what should be the decision for the Levene's test for homogeneity of variances at a 5% level of significance?

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

Question 73

Instruction 11-9
An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows.

Referring to Instruction 11-9,the value of MSA is ________,while MSW is ________.

Question 74

Instruction 11-9
An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows.

Referring to Instruction 11-9,the among-group variation or SSA is ________.

Question 75

Instruction 11-9
An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows.

Referring to Instruction 11-9,the agronomist decided to perform an ANOVA F test.The amount of total variation or SST is ________.

Question 76

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,the within-group variation or SSW is ________.

Question 77

Instruction 11-9
An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows.

Referring to Instruction 11-9,the value of the test statistic is ________.

Question 78

Instruction 11-9
An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants 15 fields,five with each variety.She then measures the crop yield in bushels per acre.Treating this as a completely randomised design,the results are presented in the table that follows.

Referring to Instruction 11-9,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 79

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,the among-group variation or SSA is ________.

Question 80

Instruction 11-7
A hotel chain has identically sized resorts in five locations.The following data resulted from analysing the hotel guests on randomly selected days in the five locations.

Referring to Instruction 11-7,what are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?