Deck 13: Analysis of Variance and Experimental Design

Question 1

In order to determine whether or not the means of two populations are equal,

A)a t test must be performed
B)an analysis of variance must be performed
C)either a t test or an analysis of variance can be performed
D)a chi-square test must be performed

Answer 1

C

Question 2

In ANOVA,which of the following is not affected by whether or not the population means are equal?

A)
B)between-samples estimate of $\sigma$ ²
C)within-samples estimate of $\sigma$ ²
D)None of these alternatives is correct.

Answer 2

within-samples estimate of $\sigma$ ²

Question 3

In factorial designs,the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as

A)main effect
B)replication
C)interaction
D)None of these alternatives is correct.

Answer 3

C

Question 4

The required condition for using an ANOVA procedure on data from several populations is that the

A)the selected samples are dependent on each other
B)sampled populations are all uniform
C)sampled populations have equal variances
D)sampled populations have equal means

Question 5

The critical F value with 6 numerator and 60 denominator degrees of freedom at $\alpha$ = .05 is

A)3.74
B)2.25
C)2.37
D)1.96

Question 6

An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations.The degrees of freedom for the critical value of F are

A)3 and 20
B)3 and 16
C)4 and 17
D)3 and 19

Question 7

When an analysis of variance is performed on samples drawn from K populations,the mean square between treatments (MSTR)is

A)SSTR/n_T
B)SSTR/(n_T - 1)
C)SSTR/K
D)SSTR/(K - 1)

Question 8

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is K,the mean square within treatments is

A)SSE/(n_T - K)
B)SSTR/(n_T - K)
C)SSE/(K - 1)
D)SSE/K

Question 9

An experimental design where the experimental units are randomly assigned to the treatments is known as

A)factor block design
B)random factor design
C)completely randomized design
D)None of these alternatives is correct.

Question 10

A term that means the same as the term "variable" in an ANOVA procedure is

A)factor
B)treatment
C)replication
D)variance within

Question 11

The variable of interest in an ANOVA procedure is called

A)a partition
B)a treatment
C)either a partition or a treatment
D)a factor

Question 12

In an analysis of variance problem involving 3 treatments and 10 observations per treatment,SSE = 399.6.The MSE for this situation is

A)133.2
B)13.32
C)14.8
D)30.0

Question 13

The F ratio in a completely randomized ANOVA is the ratio of

A)MSTR/MSE
B)MST/MSE
C)MSE/MSTR
D)MSE/MST

Question 14

The mean square is the sum of squares divided by

A)the total number of observations
B)its corresponding degrees of freedom
C)its corresponding degrees of freedom minus one
D)None of these alternatives is correct.

Question 15

In the analysis of variance procedure (ANOVA),"factor" refers to

A)the dependent variable
B)the independent variable
C)different levels of a treatment
D)the critical value of F

Question 16

In the ANOVA,treatment refers to

A)experimental units
B)different levels of a factor
C)the dependent variable
D)applying antibiotic to a wound

Question 17

The number of times each experimental condition is observed in a factorial design is known as

A)partition
B)replication
C)experimental condition
D)factor

Question 18

The ANOVA procedure is a statistical approach for determining whether or not

A)the means of two samples are equal
B)the means of two or more samples are equal
C)the means of more than two samples are equal
D)the means of two or more populations are equal

Question 19

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations.The degrees of freedom for the critical value of F are

A)6 numerator and 20 denominator degrees of freedom
B)5 numerator and 20 denominator degrees of freedom
C)5 numerator and 114 denominator degrees of freedom
D)6 numerator and 20 denominator degrees of freedom

Question 20

In an analysis of variance problem if SST = 120 and SSTR = 80,then SSE is

A)200
B)40
C)80
D)120

Question 21

Exhibit 13-2

Refer to Exhibit 13-2.The mean square between treatments equals

A)288
B)518.4
C)1,200
D)8,294.4

Question 22

An ANOVA procedure is used for data obtained from five populations.five samples,each comprised of 20 observations,were taken from the five populations.The numerator and denominator (respectively)degrees of freedom for the critical value of F are

A)5 and 20
B)4 and 20
C)4 and 99
D)4 and 95

Question 23

In a completely randomized design involving three treatments,the following information is provided:

The overall mean for all the treatments is

A)7.00
B)6.67
C)7.25
D)4.89

Question 24

The critical F value with 8 numerator and 29 denominator degrees of freedom at $\alpha$ = 0.01 is

A)2.28
B)3.20
C)3.33
D)3.64

Question 25

In an analysis of variance,one estimate of $\sigma$ ² is based upon the differences between the treatment means and the

A)means of each sample
B)overall sample mean
C)sum of observations
D)populations have equal means

Question 26

Exhibit 13-2

Refer to Exhibit 13-2.The null hypothesis is to be tested at the 5% level of significance.The p-value is

A)greater than 0.10
B)between 0.10 to 0.05
C)between 0.05 to 0.025
D)between 0.025 to 0.01

Question 27

Exhibit 13-2

Refer to Exhibit 13-2.The sum of squares due to error equals

A)14.4
B)2,073.6
C)5,760
D)6,000

Question 28

Exhibit 13-1

Refer to Exhibit 13-1.The mean square between treatments (MSTR)equals

A)400
B)500
C)1,687.5
D)2,250

Question 29

In a completely randomized design involving four treatments,the following information is provided.

The overall mean (the grand mean)for all treatments is

A)40.0
B)37.3
C)48.0
D)37.0

Question 30

Exhibit 13-2

Refer to Exhibit 13-2.The null hypothesis

A)should be rejected
B)should not be rejected
C)should be revised
D)None of these alternatives is correct.

Question 31

Which of the following is not a required assumption for the analysis of variance?

A)The random variable of interest for each population has a normal probability distribution.
B)The variance associated with the random variable must be the same for each population.
C)At least 2 populations are under consideration.
D)Populations have equal means.

Question 32

An experimental design that permits statistical conclusions about two or more factors is a

A)randomized block design
B)factorial design
C)completely randomized design
D)randomized design

Question 33

The process of allocating the total sum of squares and degrees of freedom is called

A)factoring
B)blocking
C)replicating
D)partitioning

Question 34

An ANOVA procedure is used for data obtained from four populations.Four samples,each comprised of 30 observations,were taken from the four populations.The numerator and denominator (respectively)degrees of freedom for the critical value of F are

A)3 and 30
B)4 and 30
C)3 and 119
D)3 and 116

Question 35

Exhibit 13-1

Refer to Exhibit 13-1.The null hypothesis is to be tested at the 5% level of significance.The p-value is

A)less than .01
B)between .01 and .025
C)between .025 and .05
D)between .05 and .10

Question 36

Exhibit 13-2


-Refer to Exhibit 13-2.The null hypothesis for this ANOVA problem is

A) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄
B) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄= $\mu$ ₅
C) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄= $\mu$ ₅= $\mu$ ₆
D) $\mu$ ₁= $\mu$ ₂= ...= $\mu$ ₂₀

Question 37

Exhibit 13-1

Refer to Exhibit 13-1.The test statistic to test the null hypothesis equals

A)0.22
B)0.84
C)4.22
D)4.5

Question 38

Exhibit 13-2

Refer to Exhibit 13-2.The test statistic to test the null hypothesis equals

A)0.432
B)1.8
C)4.17
D)28.8

Question 39

Exhibit 13-1

Refer to Exhibit 13-1.The null hypothesis

A)should be rejected
B)should not be rejected
C)was designed incorrectly
D)None of these alternatives is correct.

Question 40

Exhibit 13-1

Refer to Exhibit 13-1.The mean square within treatments (MSE)equals

A)400
B)500
C)1,687.5
D)2,250

Question 41

Exhibit 13-6
Part of an ANOVA table is shown below.

Refer to Exhibit 13-6.The number of degrees of freedom corresponding to between treatments is

A)18
B)2
C)4
D)3

Question 42

Exhibit 13-3
To test whether or not there is a difference between treatments A,B,and C,a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below.

Refer to Exhibit 13-3.The mean square between treatments (MSTR)equals

A)1.872
B)5.86
C)34
D)36

Question 43

Exhibit 13-3
To test whether or not there is a difference between treatments A,B,and C,a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below.

Refer to Exhibit 13-3.The test statistic to test the null hypothesis equals

A)0.944
B)1.059
C)3.13
D)19.231

Question 44

Exhibit 13-5
Part of an ANOVA table is shown below.

Refer to Exhibit 13-5.The mean square between treatments (MSTR)is

A)20
B)60
C)300
D)15

Question 45

Exhibit 13-4
In a completely randomized experimental design involving five treatments,13 observations were recorded for each of the five treatments (a total of 65 observations).The following information is provided.

Refer to Exhibit 13-4.The sum of squares within treatments (SSE)is

A)1,000
B)600
C)200
D)1,600

Question 46

Exhibit 13-3
To test whether or not there is a difference between treatments A,B,and C,a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below.

Refer to Exhibit 13-3.The null hypothesis is to be tested at the 1% level of significance.The p-value is

A)greater than 0.1
B)between 0.1 to 0.05
C)between 0.05 to 0.025
D)between 0.025 to 0.01

Question 47

Exhibit 13-4
In a completely randomized experimental design involving five treatments,13 observations were recorded for each of the five treatments (a total of 65 observations).The following information is provided.

Refer to Exhibit 13-4.If at 95% confidence we want to determine whether or not the means of the five populations are equal,the p-value is

A)between 0.05 to 0.10
B)between 0.025 to 0.05
C)between 0.01 to 0.025
D)less than 0.01

Question 48

Exhibit 13-4
In a completely randomized experimental design involving five treatments,13 observations were recorded for each of the five treatments (a total of 65 observations).The following information is provided.

Refer to Exhibit 13-4.The number of degrees of freedom corresponding to within treatments is

A)60
B)59
C)5
D)4

Question 49

Exhibit 13-5
Part of an ANOVA table is shown below.

Refer to Exhibit 13-5.The mean square within treatments (MSE)is

A)60
B)15
C)300
D)20

Question 50

Exhibit 13-6
Part of an ANOVA table is shown below.

Refer to Exhibit 13-6.The number of degrees of freedom corresponding to within treatments is

A)22
B)4
C)5
D)18

Question 51

Exhibit 13-5
Part of an ANOVA table is shown below.

Refer to Exhibit 13-5.If at 95% confidence,we want to determine whether or not the means of the populations are equal,the p-value is

A)between 0.01 to 0.025
B)between 0.025 to 0.05
C)between 0.05 to 0.1
D)greater than 0.1

Question 52

Exhibit 13-4
In a completely randomized experimental design involving five treatments,13 observations were recorded for each of the five treatments (a total of 65 observations).The following information is provided.

Refer to Exhibit 13-4.The mean square between treatments (MSTR)is

A)3.34
B)10.00
C)50.00
D)12.00

Question 53

Exhibit 13-3
To test whether or not there is a difference between treatments A,B,and C,a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below.

Refer to Exhibit 13-3.The null hypothesis

A)should be rejected
B)should not be rejected
C)should be revised
D)None of these alternatives is correct.

Question 54

Exhibit 13-5
Part of an ANOVA table is shown below.

Refer to Exhibit 13-5.The test statistic is

A)2.25
B)6
C)2.67
D)3

Question 55

Exhibit 13-4
In a completely randomized experimental design involving five treatments,13 observations were recorded for each of the five treatments (a total of 65 observations).The following information is provided.

Refer to Exhibit 13-4.The test statistic is

A)0.2
B)5.0
C)3.75
D)15

Question 56

Exhibit 13-3
To test whether or not there is a difference between treatments A,B,and C,a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below.


-Refer to Exhibit 13-3.The null hypothesis for this ANOVA problem is

A) $\mu$ ₁= $\mu$ ₂
B) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃
C) $\mu$ ₁= $\mu$ ₂= $\mu$ ₃= $\mu$ ₄
D) $\mu$ ₁= $\mu$ ₂= ...= $\mu$ ₁₂

Question 57

Exhibit 13-4
In a completely randomized experimental design involving five treatments,13 observations were recorded for each of the five treatments (a total of 65 observations).The following information is provided.

Refer to Exhibit 13-4.The number of degrees of freedom corresponding to between treatments is

A)60
B)59
C)5
D)4

Question 58

Exhibit 13-6
Part of an ANOVA table is shown below.

Refer to Exhibit 13-6.The mean square between treatments (MSTR)is

A)36
B)16
C)64
D)15

Question 59

Exhibit 13-4
In a completely randomized experimental design involving five treatments,13 observations were recorded for each of the five treatments (a total of 65 observations).The following information is provided.

Refer to Exhibit 13-4.The mean square within treatments (MSE)is

A)50
B)10
C)200
D)600

Question 60

Exhibit 13-3
To test whether or not there is a difference between treatments A,B,and C,a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below.

Refer to Exhibit 13-3.The mean square within treatments (MSE)equals

A)1.872
B)5.86
C)34
D)36

Question 61

Random samples were selected from three populations.The data obtained are shown below.Please note that the sample sizes are not equal.

a.Compute the overall mean.
b.At 95% confidence,test to see if there is a significant difference among the means.

Question 62

Information regarding the starting salaries (in $1,000)of samples of students in four different majors is given below.

a.Compute the overall sample mean.
b.Set up the ANOVA table for this problem including the test statistic.
c.At 95% confidence,determine the critical value of F.
d.Using the critical value approach,test to determine whether there is a significant difference in the means of the three populations.
e.Determine the p-value and use it for the test.

Question 63

Exhibit 13-7
The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations.

Refer to Exhibit 13-7.The conclusion of the test is that the means

A)are equal
B)may be equal
C)are not equal
D)None of these alternatives is correct.

Question 64

In order to compare the life expectancies of three different brands of printers,eight printers of each brand were randomly selected.Information regarding the three brands is shown below.

a.Compute the overall mean.
b.State the null and alternative hypotheses to be tested.
c.Show the complete ANOVA table for this test including the test statistic.
d.The null hypothesis is to be tested at 95% confidence.Determine the critical value for this test.What do you conclude?
e.Determine the p-value and use it for the test.

Question 65

Exhibit 13-6
Part of an ANOVA table is shown below.

Refer to Exhibit 13-6.The conclusion of the test is that the means

A)are equal
B)may be equal
C)are not equal
D)None of these alternatives is correct.

Question 66

Three universities administer the same comprehensive examination to the recipients of MS degrees in psychology.From each institution,a random sample of MS recipients was selected,and these recipients were then given the exam.The following table shows the scores of the students from each university.Note that the sample sizes are not equal.

a.Compute the overall mean.
b.At $\alpha$ = 0.01,test to see if there is any significant difference in the average scores of the students from the three universities.Use both the critical value and p-value approaches.

Question 67

Random samples were selected from three populations.The data obtained are shown below.Please note that the sample sizes are not equal.

a.Compute the overall mean.
b.At 95% confidence using the critical value and p-value approach,test to see if there is a significant difference among the means.

Question 68

Exhibit 13-7
The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations.

Refer to Exhibit 13-7.The number of degrees of freedom corresponding to within treatments is

A)12
B)2
C)3
D)15

Question 69

Exhibit 13-7
The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations.

Refer to Exhibit 13-7.The computed test statistics is

A)32
B)8
C)0.667
D)4

Question 70

The test scores for selected samples of sociology students who took the course from three different instructors are shown below.

At $\alpha$ = 0.05,test to see if there is a significant difference among the averages of the three groups.Use both the critical value and p-value approaches.

Question 71

Guitars R.US has three stores located in three different areas.Random samples of the sales of the three stores (in $1000)are shown below.

a.Compute the overall mean.
b.State the null and alternative hypotheses to be tested.
c.Show the complete ANOVA table for this test including the test statistic.
d.The null hypothesis is to be tested at 95% confidence.Determine the critical value for this test.What do you conclude?
e.Determine the p-value and use it for the test.

Question 72

Exhibit 13-7
The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations.

Refer to Exhibit 13-7.If at 95% confidence,we want to determine whether or not the means of the populations are equal,the p-value is

A)between 0.01 to 0.025
B)between 0.025 to 0.05
C)between 0.05 to 0.1
D)greater than 0.1

Question 73

Information regarding the ACT scores of samples of students in three different majors is given below.

a.Compute the overall sample mean.
b.Set up the ANOVA table for this problem including the test statistic.
c.At 95% confidence,determine the critical value of F.
d.Using the critical value approach,test to determine whether there is a significant difference in the means of the three populations.
e.Determine the p-value and use it for the test.

Question 74

Exhibit 13-7
The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations.

Refer to Exhibit 13-7.The mean square between treatments (MSTR)is

A)36
B)16
C)8
D)32

Question 75

The heating bills for a selected sample of houses using various forms of heating are given below.(Values are in dollars. )

a.At $\alpha$ = 0.05,test to see if there is a significant difference among the average heating bills of the homes.Use the p-value approach.
b.Test the above hypotheses using the critical value approach.Let $\alpha$ = .05.

Question 76

In a completely randomized experimental design,7 experimental units were used for the first treatment,9 experimental units for the second treatment,and 14 experimental units for the third treatment.Part of the ANOVA table for this experiment is shown below.

a.Fill in all the blanks in the above ANOVA table.
b.At 95% confidence using both the critical value and p-value approaches,test to see if there is a significant difference among the means.

Question 77

Exhibit 13-6
Part of an ANOVA table is shown below.

Refer to Exhibit 13-6.If at 95% confidence we want to determine whether or not the means of the populations are equal,the p-value is

A)greater than 0.1
B)between 0.05 to 0.1
C)between 0.025 to 0.05
D)less than 0.01

Question 78

Exhibit 13-7
The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations.

Refer to Exhibit 13-7.The number of degrees of freedom corresponding to between treatments is

A)12
B)2
C)3
D)4

Question 79

In a completely randomized experimental design,18 experimental units were used for the first treatment,10 experimental units for the second treatment,and 15 experimental units for the third treatment.Part of the ANOVA table for this experiment is shown below.

a.Fill in all the blanks in the above ANOVA table.
b.At 95% confidence,test to see if there is a significant difference among the means.

Question 80

Six observations were selected from each of three populations.The data obtained is shown below.

Test at the $\alpha$ = 0.05 level to determine if there is a significant difference in the means of the three populations.Use both the critical value and the p-value approaches.