Deck 15: Analysis of Variance

Question 1

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below:

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

Is there sufficient evidence to reject H₀ that the average between programs A,B,and C regions is the same?

A)Unable to reject H₀ for α < 0.10.
B)Reject H₀ for α = 0.10.
C)Reject H₀ for α = 0.01.
D)Reject H₀ for α = 0.05.

Answer 1

Unable to reject H₀ for α < 0.10.

Question 2

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G."

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

What value should replace "F"?

A)5.777
B)6.885
C)6.331
D)4.695

Answer 2

5.777

Question 3

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA: Single Factor
SUMMARY

ANOVA

The mean square within groups is equal to:

A)10.937
B)10.466
C)11.408
D)11.173

Answer 3

10.466

Question 4

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA: Single Factor
SUMMARY

ANOVA

The value of the test statistic F is equal to:

A)1.95
B)1.89
C)2.09
D)2.04

Question 5

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G."

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

What value should replace "D"?

A)11
B)12
C)13
D)10

Question 6

In a one-way ANOVA with n observations and k independent samples,the within-groups sum of squares is:

A)referred to as the between-groups sum of squares,denoted by SSG.
B)referred to as the error sum of squares,denoted by SSW.
C)calculated by dividing SSG by (k - 1).
D)calculated by dividing SSW by (n - k).

Question 7

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses.

What is the value of "B"?

A)6
B)5
C)3
D)2

Question 8

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA: Single Factor
SUMMARY

ANOVA

The between groups sum of squares is equal to:

A)76.801
B)65.622
C)58.718
D)72.329

Question 9

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G."

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

What value should replace "E"?

A)11.344
B)10.886
C)9.568
D)8.822

Question 10

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G."

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

What value should replace "B"?

A)21.56
B)9.29
C)23.64
D)17.44

Question 11

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA: Single Factor
SUMMARY

ANOVA

The p-value for the F-test statistic is approximately equal to ________.(Hint: Use Excel)

A)0.01
B)0.05
C)0.005
D)0.13

Question 12

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G."

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

What value should replace "A"?

A)19.92
B)318.8
C)225.4
D)64.46

Question 13

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA: Single Factor
SUMMARY

ANOVA

The total number of degrees of freedom is equal to:

A)25
B)23
C)24
D)26

Question 14

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G."

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

What value should replace "C"?

A)12
B)9
C)6
D)3

Question 15

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses.

What is the value of "A"?

A)6
B)5
C)3
D)2

Question 16

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below with missing values,identified by "A" through "G."

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

What value should "G" have?

A)4.695
B)5.777
C)6.331
D)6.885

Question 17

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below:

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

Is there sufficient evidence to reject H₀ that the average between different regions is the same?

A)Reject H₀ for α = 0.01.
B)Reject H₀ for α = 0.005.
C)Reject H₀ for α = 0.05.
D)Unable to reject H₀ for α < 0.10.

Question 18

In a two-way ANOVA,with one observation per cell,if there are 5 groups and 3 blocks,then the total number of observations is:

A)15
B)10
C)12
D)8

Question 19

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA: Single Factor
SUMMARY

ANOVA

The average for Group 1 is equal to:

A)13.708
B)12.433
C)13.256
D)11.714

Question 20

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The results of a two-factor ANOVA without replication are displayed below:

ANOVA: Two-Factor Without Replication
SUMMARY

ANOVA

What is the average over all rows and columns?

A)753.25
B)756.75
C)750.75
D)751.25

Question 21

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.

What is the value of "H"?

A)3.66
B)2.95
C)1.24
D)0.81

Question 22

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses.

What is the value of "C"?

A)6
B)5
C)3
D)2

Question 23

Is there sufficient evidence to reject the null hypothesis that there is no difference between the different types of light bulbs?

A)Unable to reject H₀ for α < 0.10
B)Reject H₀ for α = 0.01
C)Unable to reject H₀ for α > 0.10
D)Reject H₀ for α = 0.05

Question 24

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.

What is the value of "C"?

A)6
B)4
C)2
D)1

Question 25

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses.

What is the value of "G"?

A)1.350
B)1.192
C)1.421
D)1.820

Question 26

Which of the following expressions in a one-way ANOVA,with n observations and k independent samples,is used to calculate the within-groups mean square?

A)MSW / MSG
B)MSG / MSW
C)SSW / (n - k)
D)SSW / (k - 1)

Question 27

Is there sufficient evidence to reject α that there is no difference between the analysts' forecasts?

A)Reject H₀ for α = 0.05
B)Unable to reject H₀ for α > 0.10
C)Reject H₀ for α = 0.01
D)Unable to reject H₀ for α < 0.10

Question 28

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses.

What is the value of "D"?

A)15.20
B)23.24
C)12.77
D)38.44

Question 29

Is there sufficient evidence to reject the null hypothesis that there is no difference between the different manufacturers of light bulbs?

A)Reject H₀ for α = 0.01
B)Unable to reject H₀ for α > 0.10
C)Reject H₀ for α = 0.05
D)Unable to reject H₀ for α < 0.10

Question 30

Is there sufficient evidence to reject H₀ that there is no difference between the stocks?

A)Unable to reject H₀ for α < 0.10
B)Reject H₀ for α = 0.05
C)Unable to reject H₀ for α > 0.10
D)Reject H₀ for α = 0.01

Question 31

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses.

What is the value of "E"?

A)15.20
B)23.24
C)12.77
D)38.44

Question 32

Which of the following expressions in a one-way ANOVA experiment,with n observations and k independent samples,is used to calculate the F test statistic?

A)SSW / (n - k)
B)SSW / (k - 1)
C)MSW / MSG
D)MSG / MSW

Question 33

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.

What is the value of "E"?

A)484.67
B)727.00
C)246.33
D)198.83

Question 34

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.

What is the value of "A"?

A)7
B)5
C)3
D)2

Question 35

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses.

What is the value of "H"?

A)1.350
B)1.190
C)1.421
D)1.823

Question 36

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.

What is the value of "F"?

A)484.67
B)727.00
C)246.33
D)198.83

Question 37

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.

What is the value of "G"?

A)1.24
B)3.66
C)2.95
D)0.81

Question 38

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.

What is the value of "B"?

A)7
B)5
C)3
D)2

Question 39

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A consumer group wanted to examine how long different life bulbs last.They selected three different light bulbs (60 watt,75 watt and 100 watt)from four different manufacturers.They generated the following statistics from the data.

What is the value of "D"?

A)484.67
B)727.00
C)246.99
D)198.83

Question 40

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Four stock analysts were asked to predict earnings for three different stocks for the next year.The following ANOVA table with missing values identified by "A" through "H" summarizes the responses.

What is the value of "F"?

A)15.20
B)23.24
C)12.77
D)38.44

Question 41

What is the mean square value for Blocks?

A)429.63
B)43.14
C)153.89
D)307.78

Question 42

In a Kruskal-Wallis test at the 5% significance level,there are four samples and the value of the test statistic is calculated as W = 8.79.The most accurate statement that can be made about the p-value is that it is:

A)greater than 0.10
B)greater than 0.05 but smaller than 0.10
C)greater than 0.05
D)greater than 0.025 but smaller than 0.05

Question 43

What is the total degrees of freedom for the test?

A)10
B)14
C)16
D)20

Question 44

Which of the following is the calculated p-value for Blocks? (Hint: Use Excel)

A)0.52
B)0.93
C)0.20
D)0.72

Question 45

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A randomized block design ANOVA has five treatments and three blocks.The analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA

Determine the sum of squares value for Treatments.

A)86.28
B)307.78
C)345.13
D)153.89

Question 46

A randomized block experiment having five treatments and six blocks produced the following values: SST = 1446,SSG = 287 and SSE = 180.The value of SSB is calculated to be:

A)30
B)979
C)467
D)20

Question 47

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A randomized block design ANOVA has five treatments and three blocks.The analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA

What is the degrees of freedom value for Rows?

A)5
B)4
C)2
D)1

Question 48

What is the mean square value for Error?

A)429.63
B)121.85
C)394.06
D)129.42

Question 49

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A randomized block design ANOVA has five treatments and three blocks.The analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA

What is the degrees of freedom value for Blocks?

A)8
B)2
C)4
D)5

Question 50

A randomized block design ANOVA has five treatments and four blocks.The computed test statistic (value ofF)is 4.35.With a 0.05 significance level,the appropriate table value and conclusion will,respectively,be:

A)14.37;fail to reject the null hypothesis.
B)3)11;fail to reject the null hypothesis.
C)3)26;fail to reject the null hypothesis.
D)3)26;reject the null hypothesis.

Question 51

The degrees of freedom for the F test in a one-way ANOVA,with n observations and k independent samples,are:

A)(k - 1)and (n - k)
B)(n - 1)and (n - k)
C)(k - n)and (n - 1)
D)(k - n)and (k - 1)

Question 52

The value of the test statistic F at Treatments is:

A)4.46
B)3.84
C)0.20
D)0.72

Question 53

The degrees of freedom for the interaction term in a two-way ANOVA,with k groups,H blocks and L number of observations per cell,are:

A)k - 1
B)H - 1
C)(k - 1)(H - 1)
D)K-H-L + 1

Question 54

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A randomized block design ANOVA has five treatments and three blocks.The analysis of variance table is displayed below with missing values,denoted by asterisks.
ANOVA

What is the degrees of freedom for Error?

A)8
B)9
C)10
D)15

Question 55

What is the total for the sum of squares?

A)2476.33
B)960.7
C)3437.02
D)4397.72

Question 56

The value of the test statistic F at Blocks is:

A)3.84
B)4.46
C)0.20
D)0.72

Question 57

Which of the following is the calculated p-value for Treatments? (Hint: Use Excel)

A)0.52
B)0.93
C)0.20
D)0.72

Question 58

A randomized block design with four treatments and five blocks produced the following sum of squares values: SST = 1951,SSG = 349,SSB = 1414.Based on this data,the value of the SSE is calculated to be:

A)188
B)537
C)1602
D)1763

Question 59

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,on the average,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. Package 1: 12,14,9,11,and 16 Package 2: 2,4,7,3,and 1
Package 3: 10,9,6,10,and 12 Package 4: 7,6,6,15,and 12
Which of the following tests is appropriate for testing the software's use?

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 between matched pairs

Question 60

Which of the following is a nonparametric alternative to a one-way ANOVA test?

A)Jarque-Bera test
B)Wilcoxon rank sum test
C)Kuiper's test
D)Kruskal-Wallis test

Question 61

When conducting sample variance using the Kruskal-Wallis test,the sample values are pooled together randomly.

Question 62

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a two-way ANOVA,there are 5 groups,3 blocks,and two observations per cell.
The number of degrees of freedom for between blocks is:

A)8
B)6
C)4
D)2

Question 63

In a two-way analysis of variance with several observations per cell,the total sum of squares is calculated using the formula SSG + SSB + SSI / SSE.

Question 64

In a one-way ANOVA,if the ratio F =MSG / MSW is quite close to 1.0,there is little cause to doubt the null hypothesis of equality of population mean.

Question 65

Both one-way and two-way ANOVA tests calculate interactions between groups and blocks.

Question 66

The Kruskal-Wallis test for the difference in population means is based on the ranks of the sample observations.

Question 67

In a two-way analysis of variance,the number of degrees of freedom is determined by the number of groups and blocks.

Question 68

In a one-way ANOVA,if the variability between groups is large compared to the variability within groups,we suspect the null hypothesis of equality of population means to be false.

Question 69

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a two-way ANOVA,there are 5 groups,3 blocks,and two observations per cell.
The number of degrees of freedom for between groups is:

A)8
B)6
C)4
D)2

Question 70

The value for F_12,5,0.05 in a two-way ANOVA is found to be 5.06.

Question 71

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a two-way ANOVA,there are 5 groups,3 blocks,and two observations per cell.
The number of degrees of freedom for the interaction term is:

A)8
B)6
C)4
D)2

Question 72

In a two-way analysis of variance,the mean squares are obtained by dividing the sums of squares by their associated number of observations.

Question 73

In a one-way ANOVA,all the populations may or may not be normally distributed.

Question 74

The sampling distribution of the Kruskal-Wallis test statistic is well approximated by the:

A)normal distribution.
B)chi-square distribution with k - 1 degrees of freedom,where k is the number of populations.
C)F- distribution with 1 and k - 1 degrees of freedom,where k is the number of Populations.
D)Student's t distribution with n - 1 degrees of freedom.

Question 75

Blocking variables cannot be used in a two-way ANOVA having randomized blocks.

Question 76

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a two-way ANOVA,there are 5 groups,3 blocks,and two observations per cell.
The number of degrees of freedom for error is:

A)29
B)15
C)8
D)4

Question 77

In a two-way ANOVA,with one observation per cell,if there are 4 groups and 3 blocks,then there are a total of 7 observations.

Question 78

The total number of degrees of freedom is:

A)29
B)15
C)8
D)4

Question 79

In a two-way ANOVA with more than one observation in a cell,interaction occurs between groups and blocks due to normal distribution of differences between them.

Question 80

In a one-way ANOVA with randomized blocks,the additional blocks are also known as blocking variables.