Deck 13: Experimental Design and Analysis of Variance

Question 1

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

Answer 1

C

Question 2

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

Answer 2

D

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

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

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

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 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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

In an analysis of variance where the total sample size for the experiment is n_T 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 16

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)
E)None of these alternatives is correct.

Question 17

In the ANOVA, treatment refers to

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

Question 18

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

A)2.87
B)3.24
C)4.08
D)8.7

Question 19

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 20

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 21

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 22

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 critical value from the table is

A)4.26
B)8.02
C)16.69
D)99.39

Question 23

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 24

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 25

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 26

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 27

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

A)
B)between-samples estimate of²
C)within-samples estimate of²
D)None of these alternatives is correct.

Question 28

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 29

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 30

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 31

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 32

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 33

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 34

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 35

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

A)2.71
B)2.87
C)5.19
D)5.8

Question 36

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 37

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

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

Question 38

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

Question 39

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 40

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 41

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 42

Exhibit 13-5
Part of an ANOVA table is shown below.
Refer to Exhibit 13-5. The conclusion of the test is that the means

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

Question 43

Exhibit 13-4
In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
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 44

Exhibit 13-4
In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
Refer to Exhibit 13-4. The conclusion of the test is that the five means

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

Question 45

Exhibit 13-5
Part of an ANOVA table is shown below.
Refer to Exhibit 13-5. If at a 5% level of significance, we want to determine whether or not the means of the populations are equal, the critical value of F is

A)2.53
B)19.48
C)3.29
D)5.86

Question 46

Exhibit 13-7
The following is part of an ANOVA table, which was the results of 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 47

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 48

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
Refer to Exhibit 13-7. If at a 5% level of significance, we want to determine whether or not the means of the populations are equal, the critical value of F is

A)4.75
B)19.41
C)3.16
D)1.96

Question 49

Exhibit 13-4
In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
Refer to Exhibit 13-4. The mean square within treatments (MSE) is

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

Question 50

Exhibit 13-7
The following is part of an ANOVA table, which was the results of 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 51

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 52

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 53

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 54

Exhibit 13-4
In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
Refer to Exhibit 13-4. The sum of squares within treatments (SSE) is

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

Question 55

Exhibit 13-4
In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
Refer to Exhibit 13-4. If at a 5% level of significance we want to determine whether or not the means of the five populations are equal, the critical value of F is

A)2.53
B)19.48
C)4.98
D)39.48

Question 56

Exhibit 13-4
In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
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 57

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 58

Exhibit 13-7
The following is part of an ANOVA table, which was the results of 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 59

Exhibit 13-4
In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
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 60

Exhibit 13-6
Part of an ANOVA table is shown below.
Refer to Exhibit 13-6. If at a 5% significance level we want to determine whether or not the means of the populations are equal, the critical value of F is

A)5.80
B)2.93
C)3.16
D)2.90

Question 61

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
In testing for the equality of k population means, the number of treatments is

A) k
B) k - 1
C) n_T
D) n_T - k

Question 62

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
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 63

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.

-If we are testing for the equality of 3 population means, we should use the

A) test statistic F
B) test statistic t
C) test statistic z
D) test statistic $\chi$ ²

Question 64

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
In an analysis of variance, one estimate of 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 65

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.

-Six observations were selected from each of three populations. The data obtained is shown below:
Test at $\alpha$ = 0.05 level to determine if there is a significant difference in the means of the three populations.

Question 66

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
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
E)None of these alternatives is correct.

Question 67

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
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 a 5% level of significance, 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, which was the results of three treatments and a total of 15 observations.
Random samples were selected from three populations. The data obtained are shown below. At a 5% level of significance, test to see if there is a significant difference in the means of the three populations. (Please note that the sample sizes are not equal.)

Question 69

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
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 70

Exhibit 13-7
The following is part of an ANOVA table, which was the results of 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 71

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
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: At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores. (Please note that the sample sizes are not equal.)

Question 72

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
Information regarding the ACT scores of samples of students in four different majors are given below.
a.Set up the ANOVA table for this problem.
b.At a 5% level of significance, test to determine whether there is a significant difference in the means of the four populations.

Question 73

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
Information regarding the ACT scores of samples of students in three different majors are given below.
a.Set up the ANOVA table for this problem.
b.At a 5% level of significance, test to determine whether there is a significant difference in the means of the three populations.

Question 74

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.

-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 75

Exhibit 13-7
The following is part of an ANOVA table, which was the results of 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 76

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
The manager of Young Corporation wants to determine whether or not the type of work schedule for her employees has any effect on their productivity. She has selected 15 production employees at random and then randomly assigned 5 employees to each of the 3 proposed work schedules. The following table shows the units of production (per week) under each of the work schedules. At a 5% level of significance determine if there is a significant difference in the mean weekly units of production for the three types of work schedules.

Question 77

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
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 a 5% level of significance, test to see if there is a significant difference among the means.

Question 78

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
Random samples were selected from three populations. The data obtained are shown below. At a 5% level of significance, test to see if there is a significant difference in the means of the three populations. (Please note that the sample sizes are not equal.)

Question 79

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.
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 80

Exhibit 13-7
The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations.

-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.